John  Sv;ett 


From  the  collection  of  the 

7    n 
z_    m 

o  Prelinger 

i     a 

Uibrary 


San  Francisco,  California 
2006 


ELEMENTARY  CLASS  BOOK 


ASTRONOMY: 


IN   WTTTCH 


MATHEMATICAL  DEMONSTRATIONS  ARE  OMITTED. 


BY  H.  N.  ROBINSON,  LL.  D. 

FORMERLY  PEOFESSOR  OF  MATHEMATICS  IN  THE  UNITED  STATES  NAYY  ; 

AUTHOR   OF  A  TREATISE  ON  ARITHMETIC,  ALGEBRA,  GEOMETRY, 

TRIGONOMETRY,  SURVEYING,  CALCULUS,  40.  40. 


NEW    YORK: 

IVISON,  PHINNEY  &  CO,  48  &  50  WALKER  STREET. 
CHICAGO:  S.  C.  GRTGGS  &  CO.,  39  &  41  LAKE  ST. 

CINCINNATI  :    MOORK,  WIL6TACH,  KKY8   A   CO.      ST.    LOUIS  I    KKITH  If  WOODS, 
PHILADELPHIA.  :    BOWKR,    BARNES    k    CO.       BUFFALO:    PUINNET   A   OO. 

1860. 


R  0  B  I  N  S  O  N'S 


The  most  COMPLETE,  most  PRACTICAL,  and  most  SCIENTIFIC  SERIES  of 
MATHEMATICAL  TEXT-BOOKS  ever  issued  in  this  country 


t  Robinson's  Progressive  Table  Book,  » 

IL  Robinson's  Progressive  Primary  Arithmetic,-       - 

in.  Robinson's  Progressive  Intellectual  Arithmetic,   -       -      - 

IV.  Robinson's  Rudiments  of  Written  Arithmetic,  « 

V.  Robinson's  Progressive  Practical  Arithmetic,  • 

VL  Robinson's  Key  to  Practical  Arithmetic, 

VIL  Robinson's  Progressive  Higher  Arithmetic,  • 

VIIL  Robinson's  Key  to  Higher  Arithmetic, 

IX.  Robinson's  New  Elementary  Algebra,  • 

X.  Robinson's  Key  to  Elementary  Algebra,  ----«. 

XI.  Robinson's  University  Algebra,   ------«, 

XIL  Robinson's  Key  to  University  Algebra,  *• 

XIII.  Robinson's  New  University  Algebra,  -      s 

XIV.  Robinson's  Key  to  New  University  Algebra,  • 

XV.  Robinson's  New  Geometry  and  Trigonometry,    -••••* 

XVI.  Robinson's  Surveying  and  Navigation,     - 

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XVIII.  Robinson's  Differen.  and  Int.  Calculus,  (in  preparation,)- 

XIX.  Robinson's  Elementary  Astronomy,   -       -      •       •       -      v 

XX.  Robinson's  University  Astronomy,     -       -       -      -      -      <- 

XXI.  Robinson's  Mathematical  Operations,        .-_•-« 

XXII.  Robinson's  Key  to  Geometry  and  Trigonometry,  Conia 

Sections  and  Analytical  Geometry, 


Entered,  according  to  Act  of  Congress,  in  the  year  1857,  by 
HOEATIO    N.    KOBINSON,    LL.D., 

In  the  Clerk's  Office  of  the  District  Court  of  the  United  States  for  the  Northern 
District  of  New  York. 


PREFACE 


EVERY  one  strives  to  adapt  means  to  ends,  and  when  the  author  pre- 
pared his  large  work  on  Astronomy,  he  had  no  other  end  in  view  than  to 
teach  Astronomy  to  such  as  may  be  competent  to  the  task  and  fully  pre- 
pared to  learn  it.  His  first  aim  was  to  produce  a  book  of  the  right  tone 
and  character,  without  any  regard  to  the  number  of  persons  who  might  be 
prepared  to  use  it.  That  effort  was  entirely  successful,  but  the  book  is  not 
adapted  to  the  great  mass  of  pupils,  because  it  requires  of  the  learner 
considerable  mathematical  knowledge,  and  a  corresponding  discipline  of 
mind,  therefore  but  few  persons,  comparatively  speaking,  feel  qualified  to 
study  that  book.  At  the  same  time  a  book  of  like  tone,  character,  and 
spirit,  is  demanded  by  teachers  for  the  use  of  their  more  humble  pupils, 
except  that  it  must  be  on  a  lower  mathematical  plane,  and  this  book  is  de- 
signed to  supply  that  demand. 

In  this  work  we  have  omitted  mathematical  investigations  almost  alto- 
gether. Yet  we  have  endeavored  to  retain  the  spirit  of  the  University 
edition,  and  much  of  the  plain  matter  of  fact  in  that  book  is  the  same  in 
this.  Some  of  the  more  abstruse  parts  of  the  science  are  omitted,  and 
some  of  the  more  simple  and  elementary  parts  are  more  enlarged  upon  in 
this  book,  than  in  that. 

Because  we  have  avoided  mathematical  investigations,  and  attempted  to 
adapt  our  work  to  the  common  qualifications  of  pupils,  it  must  not  be  in- 
ferred that  we  have  therefore  made  an  easy  text  book,  one  which  requires 


iv  PREFACE. 

no  particular  attention  on  the  part  of  the  reader  to  comprehend.  Astron- 
omy is  no  study  for  children — the  subject  admits  of  no  careless  reading, 
and  however  good  the  book,  and  however  well  qualified  the  teacher,  the 
student  must  take  vigorous  hold  of  the  study  for  himself,  and,  in  a  mea- 
sure, take  his  own  way  to  meet  with  success. 

Although  this  professes  to  be  but  a  primary  and  elementary  work,  it 
contains  more  than  a  mere  statement  of  astronomical  facts,  it  deduces  hid- 
den truths  from  primary  observations,  and  endeavors  to  draw  out  the  logi- 
cal powers  of  the  reader  and  make  him  feel  the  true  spirit  of  the  science. 

Science  properly  learned  is  never  forgotten,  but  science  committed  to 
memory  soon  evaporates,  and  science  cannot  be  obtained  from  books  and 
teachers  alone,  — in  addition  to  the  materials,  the  original  perceptions  and 
reasoning  powers  of  the  learner,  must  come  in  with  decided  earnestness 
and  force,  —  and  these  remarks  are  particularly  applicable  to  the  science 
of  Astronomy. 

We  make  these  remarks  to  impress  on  the  mind  of  the  teacher  the  ne- 
cessity of  giving  perfectly  sound  instruction,  and  not  be  contented  with 
memoritor  recitations,  or  the  mere  accumulation  of  facts. 

For  instance,  the  sun  is  nearer  to  the  earth  in  January  than  in  July,  but 
this  fact  alone  is  not  science,  scarcely  knowledge  —  and  it  would  be  only 
a  dead  weight  to  the  mind  to  crowd  it  into  the  memory  :  but  when  it  is 
ascertained  how  we  know  this  fact,  from  what  observation  it  was  deduced, 
and  what  logical  induction  was  applied,  then  it  becomes  another  matter, 
then  it  is  science,  and  thus  learned,  could  never  be  lost. 

Some  elementary  works  on  Astronomy  put  great  stress  on  pictorial  illus- 
trations,—  but  at  best  such  illustrations  are  little  better  than  caricatures, 
and  some  of  them  give  incorrect  impressions  ;  for  instance,  in  attempting 
to  show  the  relative  motions  of  the  sun  and  moon  in  space,  by  a  figure,  the 
moon's  motion  is  generally  represented  as  describing  loops,  when  the  true 
motion  is  progressively  onward,  and  at  all  times  concave  towards  the  sun. 


PREFACE.  r 

The  difficulty  of  giving  true  representations  on  paper,  in  Astronomy,  is  so 
great  that  the  teacher  should  be  careful  so  to  guide  the  perceptions  of  the 
learner,  that  they  be  more  truthful  and  refined  than  the  figure  can  possibly 
be,  or  the  learner  will  draw  distorted  if  not  erroneous  impressions  from 
them.  For  instance,  if  we  wished  to  make  a  correct  representation  of  the 
sun,  earth,  and  moon,  and  made  the  earth  but  one-eighth  of  an  inch  in 
diameter,  the  diameter  of  the  moon's  orbit  must  be  7j^  inches,  the  diame- 
ter of  the  moon  the  32d  part  of  an  inch,  the  diameter  of  the  earth's  orbit 
3000  inches,  or  250  feet,  and  the  diameter  of  the  sun  must  cover  14  inches. 
These  considerations  show  the  utter  impossibility  of  making  correct  as- 
tronomical representations  on  paper,  for  who  would  have  the  earth  drawn 
out  less  than  one-eighth  of  an  inch  in  diameter,  and  even  that  small  mag- 
nitude would  require  a  sheet  two  hundred  and  fifty  feet  wide,  on  which 
none  of  the  exterior  planets  could  be  drawn.  For  these  reasons  we  do  not 
place  as  much  value  on  pictorial  representations  and  astronomical  maps  as 
many  do,  and  whenever  we  make  use  of  such  things,  as  we  sometimes  do, 
we  take  much  care  that  the  impressions  drawn  from  them,  are  not  as  gross 
as  the  representations  themselves. 

In  conclusion,  we  would  remind  the  reader  that  the  subject  of  Astronomy 
is  so  vast  and  magnificent,  that  it  is  almost  as  impossible  to  do  justice  to 
it  in  composition  as  it  is  in  geometrical  diagrams.  We  have  made  no  pre- 
tensions to  delineate  the  high  mental  satisfaction  that  a  knowledge  of 
this  science  imparts  ;  we  have  only  attempted  to  guide  others  in  attaining 
that  knowledge,  and  in  this  particular  we  do  not  claim  to  have  made  a 
perfect  book,  —  far  from  it,  —  perfection  is  impossible,  decidedly  so,  when 
applied  to  a  book  ;  and  if  all  books  were  perfect,  there  would  be  little  need 
of  schools  and  teachers. 


CONTENTS. 


SECTION   I. CHAPTER   I. 

PAGE. 
Introduction , 11 

Definition  of  terms 12—17 

CHAPTER   II. 

Preliminary  observations 18 

The  north  pole  in  the  heavens  —  the  fixed  point 19 

Circumpolar  stars 21 

A  definite  index  for  the  length  of  years 24 

Wandering  stars 25 

CHAPTER   HI. 

Fixed  stars — landmarks,  <fec 26 — 28 

How  to  find  the  north  star 29 

How  to  find  any  star 30 — 33 

CHAPTER    IY. 

Time  —  and  the  measure  of  time 34 

Sideral  time  —  the  only  standard  measure  of  time 35 — 36 

Why  astronomers  commence  the  day  at  noon 37 

CHAPTER    V. 

Astronomical  instruments 38—41 

Astronomical  refraction 42 — 43 

Effects  of  refraction 44 

How  to  find  the  true  altitude  of  a  heavenly  body 45 — 46 

How  to  find  the  declination  of  a  star 47 — 49 

CHAPTER    VI. 

Scientific  method  of  finding  stars .50 — 54 

How  we  may  find  a  particular  star 54 — 56 

CHAPTER   VII. 

Fixed  and  moving  bodies 57 

Observations  showing  the  motion  of  the  wandering  stars 58 

Figure  and  magnitude  of  the  earth 59 — 63 

Unequal  pressure  on  the  earth's  surface 64 — 67 

vii 


Vlii  CONTENTS. 

SECTION    II. CHAPTER   I. 

First  consideration  in  respect  to  distance,  astronomically  speaking,  68 — 70 

Horizontal  parallax 71 — 75 

Distance  to  the  moon  —  deduced  from  parallax 76 — 78 

CHAPTER    II. 

Solar  parallax 79 

How  to  measure  the  sun's  apparent  diameter *. .  .80 — 83 

Figure  of  the  apparent  solar  orbit 84 

How  to  find  the  position  of  the  longer  axis  of  the  solar  orbit 85 — 66 

CHAPTER   UI. 

The  causes  of  the  change  of  seasons 87 — 91 

CHAPTER   IV. 

Equation  of  time 92 

Causes  which  produce  inequality  in  apparent  time 93 — 95 

Equation  table,  Ac 96—98 

CHAPTER   V. 

The  apparent  motions  of  the  planets 99 — 102 

The  sun  the  center  of  the  planetary  motions 103 — 104 

Copernicus  —  and  his  system 105 

CHAPTER    VI. 

The  Copernican  system  illustrated 106 — 107 

The  relative  distances  of  the  planets  from  the  sun  discovered.. .  .108 — 110 

The  times  of  revolution  deduced  from  observation Ill — 116 

Kepler's  laws 117 

CHAPTER   VII. 

The  transits' of  Venus  and  Mercury 118 

The  sun's  horizontal  parallax  determined 119—123 

CHAPTER    VIII. 

The  real  distance  to  the  sun  determined 124 

The  distance  of  each  planet  from  the  sun  determined 125 

The  magnitudes  of  the  planets  discovered 126 

CHAPTER   IX. 

A  general  description  of  the  solar  system 127 — 132 

A  table  of  the  asteroids 133 

The  velocity  of  light  discovered 134—137 

General  directions  to  acquire  a  correct  impression  of  distances 

and  magnitudes  in  the  solar  system 141 — 142 


CONTENTS.  ix 

SECTION   III. CHAPTER   I. 

The  moon — its  periodical  revolutions,  Ac .  143 — 144 

The  lunar  cycle,  or  golden  number 145 

The  figure  of  the  moon's  orbit,  <fec 146 

Libration  of  the  moon 147 — 151 

CHAPTER  II. 

Eclipses 152—153 

Limits  of  eclipses  from  the  nodes 154 

Periodical  eclipses 156—160 

Occultations 161 

CHAPTER   III. 

The  tides 162 

The  obvious  connection  of  the  tides  and  the  moon 162 

Tides  opposite  to  the  moon  explained 163— 1 64 

Mass  of  the  moon  determined  by  the  tides 165 

The  great  inequality  of  the  tides  explained 166 

CHAPTER  IV, 

On  comets,  —  their  general  description,  <fcc 167 

Comets,  planetary  bodies 168 

Description  of  particular  comets 169 — 172 

The  probable  effect  of  a  comet  striking  the  earth 173 

CHAPTER   V. 

On  the  peculiarities  of  the  fixed  stars 174 — 175 

Their  immense  distance  from  the  earth 176 

Thenewstarof  1572 176 

Double  and  multiple  stars 178 

Nebulae  —  and  the  milky  way '. 179 

Gradual  changes  of  the  stars  in  right  ascension  and  declination, 

caused  by  the  motion  of  the  equator  on  the  ecliptic 179 

Proper  motion  of  fixed  stars  —  how  determined 180 

CHAPTER   VI. 

Aberration  —  how  discovered  —  and  by  whom 181 

Aberration  illustrated 182 

Velocity  of  light  determined  by  aberration 182 — 183 

Aberration  —  a  proof  of  the  earth's  annual  revolution 184 

Nutation  —  its  cause  and  effects 185 

Nutation  illustrated 186 

Precession  of  the  equinoxes 188 

Precession  and  nutation  depend  on  the  same  cause,  the  spheroidal 

form  of  the  earth . .  189 — 190 


X  CONTENTS. 

SEQUEL. 

Problems  on  the  terrestrial  globe 191—196 

Problems  to  be  solved  with  or  without  the  use  of  of  the  globes. . .  196 — 202 
Various  problems  for  finding  the  latitude  of  the  observer,  by  the 

meridian  distances  of  the  heavenly  bodies 199 — 201 

Problems  to  be  solved  by  the  use  of  the  celestial  globe 202 — 205 

How  to  find  the  time  of  rising  and  setting  of  any  known 

heavenly  body 205—206 


ASTRONOMY. 


CHAPTER   I. 


INTRODUCTION. 

ASTRONOMY  is  the  science  which  treats  of  the  heavenly 
bodies,  describes  their  appearances,  determines  their  magni- 
tudes, and  discovers  the  laws  that  govern  their  motions. 

Astronomy  is  divided  into  Descriptive,  Physical,  and  Prac- 
tical. 

Descriptive  Astronomy  merely  states  facts  and  describes  ap- 
pearances. 

Physical  Astronomy  explains  the  causes  which  bring  about 
the  known  results.  It  investigates  the  laws  "which  govern  the 
celestial  motions. 

Practical  Astronomy  includes  observations,  and  all  kinds  of 
astronomical  computations,  such  as  the  distances  and  magni- 
tudes of  the  planets,  the  times  of  their  rising,  setting,  and 
coming  in  conjunction,  opposition,  &c.  <fec. 

By  astronomical  observations  men  can  determine  the  posi- 
tion of  a  ship  on  sea,  and  this  branch  of  astronomy  is  called 
Nautical  Astronomy,  and  thus  geography  and  astronomy  are 
combined,  and  no  one  can  fully  understand  geography  without 
some  aid  from  ascronomy. 

Astronomy  is  the  most  ancient  of  all  sciences,  for  the  people 
could  not  avoid  observing  the  successive  returns  of  day  and 

Define  Astronomy.  How  is  Astronomy  divided  ?  What  is  Descriptive 
Astronomy  ?  What  is  Physical  ?  What  is  Practical  ?  Are  Geography  and 
Astronomy  connected  ?  How  ?  Is  Astronomy  a  modern  science  V  Why 
is  it  allowed  to  be  the  most  ancient  science  ? 

H 


14  ELEMENTARY  ASTRONOMY. 

The  Celestial  Equator  is  the  plane  of  the  earth's  equator  con- 
ceived to  extend  into  the  heavens. 

When  the  sun,  or  any  other  heavenly  body,  meets  the  celes- 
tial equator,  it  is  said  to  be  in  the  Equinox,  and  the  equatorial 
line  in  the  heavens  is  called  the  Equinoctial. 

Latitude. — The  latitude  of  any  place  on  the  earth,  is  its  dis- 
tance from  the  equator,  measured  in  degrees  on  the  meridian, 
either  north  or  south. 

If  the  measure  is  toward  the  north,  it  is  north  latitude  ;  if 
toward  the  south,  south  latitude. 

The  distance  from  the  equator  to  the  poles  is  90  degrees  — 
one-fourth  of  a  circle  ;  and  we  shall  know  the  circumference 
of  the  whole  earth  whenever  we  can  find  the  absolute  length  of 
one  degree  on  its  surface. 

Co-Latitude. — Co-latitude  is  the  distance,  in  degrees,  of  any 
place  from  the  nearest  pole. 

The  latitude  and  co-latitude  (complement  of  the  latitude) 
must,  of  course,  always  make  90  degrees. 

Parallels  of  latitude  are  small  circles  on  the  surface  of  the 
earth,  parallel  to  the  equator. 

Every  point,  in  such  a  circle,  has  the  same  latitude. 

Longitude. — The  longitude  of  a  place,  on  the  surface  of  the 
earth,  is  the  inclination  of  its  meridian  to  some  other  meridian 
which  may  be  chosen  to  reckon  from.  English  astronomers 
and  geographers  take  the  meridian  which  runs  through  Green- 
wich Observatory,  as  the  zero  meridian. 

Other  nations  generally  take  the  meridian  of  their  principal 
observatories,  or  that  of  the  capital  of  their  country,  as  the 
first  meridian  ;  but  this  is  national  vanity,  and  creates  only 
trouble  and  confusion  :  it  is  important  that  the  whole  world 

What  do  you  understand  by  the  Celestial  Equator  ?  What  is  latitude 
on  the  earth  ?  How  is  it  measured  ?  How  many  degrees  are  there  from 
the  equator  to  the  pole  ?  If  the  earth  were  larger,  would  there  be  more 
degrees  from  the  equator  to  the  pole  ?  What  is  longitude  ?  What  meri 
dian  is  it  reckoned  from  <  Why  that  meridian  ?  Could  it  have  been  from 
any  other  ? 


INTRODUCTION.  1 5 

should  agree  on  some  one  meridian,  from  which  to  reckon  longi- 
tude ;  but  as  nature  has  designated  no  particular  one,  it  is  not 
wonderful  that  different  nations  have  chosen  different  lines. 

In  this  work,  we  shall  adopt  the  meridian  of  Greenwich  as 
the  zero  line  of  longitude,  because  most  of  the  globes  and 
maps,  and  all  the  important  astronomical  tables,  are  adapted  to 
that  meridian,  and  we  see  nothing  to  be  gained  by  changing  it. 

Declination. — Declination  refers  only  to  the  celestial  equator, 
and  is  a  leaning  or  declining,  north  or  south  of  that  line,  and  it 
is  similar  to  latitude  on  the  earth. 

Solsticial  points. — The  points,  in  the  heavens,  north  and 
south,  where  the  sun  has  its  greatest  declination,  are  the  solsti- 
cial  points. 

The  northern  point  we  call  the  Summer  Solstice,  and  the 
southern  point  the  Winter  Solstice;  the  first  is  in  longitude  90°, 
the  second  in  longitude  270°. 

As  latitude  is  reckoned  north  and  south,  so  longitude  is 
reckoned  east  and  west ;  but  it  would  add  greatly  to  syste- 
matic regularity,  and  tend  much  to  avoid  confusion  and  am- 
biguity in  computations,  were  this  mode  of  expression  aban- 
doned, and  longitude  invariably  reckoned  westward,  from  0  to 
360  degrees. 

Declination  in  the  heavens  is  similar  to  latitude  on  the  earth. 
If  a  person  were  in  20°  north  latitude  when  the  sun's  declina- 
tion was  20°  north,  the  sun  at  noon  would  then  be  in  his  zenith, 
or  pass  directly  over  his  head. 

Ecliptic. — The  ecliptic  is  a  great  circle  in  the  heavens,  along 
which  the  sun  appears  to  pass  in  a  year,  extending  from  about 
23£  degrees  of  south  declination  to  about  23^  degrees  of  north 
declination  in  the  opposite  longitude  of  the  heavens.  This 
circle  is  called  the  ecliptic,  because  all  eclipses,  both  of  the 
sun  and  moon,  take  place  when  the  moon  is  either  in  or  near  it. 

What  is  declination  ?  What  is  the  declination  of  the  north  pole  ?  What 
are  the  solsticial  points  ?  In  what  latitude  are  they  ?  What  circle  is  the 
sun  always  in  ?  Why  is  that  circle  called  the  pcliptic  ? 


16  ELEMENTARY  ASTRONOMY. 

Equator  and  Ecliptic. — The  celestial  equator  and  the  ecliptic 
are  two  great  circles,  in  the  heavens,  which  intersect  each 
other  (at  the  present  day)  by  an  angle  of  about  23°  27'  32". 

The  sun,  in  its  apparent  annual  motion,  runs  round  the  heav- 
ens, crosses  the  equator  from  the  south  to  the  north  on  the 
20th  of  March  of  each  year,  and  re-crosses  from  the  north  to 
the  south  on  the  23d  of  September. 

The  point  on  the  ecliptic  where  the  sun  meets  the  celestial 
equator  in  the  spring,  is  taken  as  the  zero  point  from  which  to 
reckon  longitude,  in  astronomy,  eastward  along  the  ecliptic. 
This  point  is  called  tfie  Vernal  Equinox. 

From  the  same  point  eastward  along  the  equator  is  reckoned 
right  ascension,  and  it  is  counted  from  0  degrees  to  360  degrees, 
or  from  0  hours  to  24  hours  ;  15  degrees  of  arc  corresponding 
to  one  hour  in  time. 

Zodiac. — Ancient  astronomers  defined  the  zodiac  to  be  a 
space  in  the  heavens  sixteen  degrees  wide,  eight  degrees  on 
each  side  of  the  ecliptic,  and  quite  round  the  sphere  :  the 
ecliptic  was  therefore  the  center  of  the  zodiac.  The  ecliptic, 
or  zodiac,  was  divided  into  twelve  signs,  called  signs  of  the 
zodiac,  each  sign  was  therefore  30°  in  extent. 

The  first  sign,  commencing  at  the  vernal  equinox,  is  called 
Aries,  and  the  character  denoting  it  is  written  thus  r)f\ 

The  sun  enters  the  12  signs  as  follows  : 

Aries  (^')  on  the  20th  of  March  ;  Taurus  (\J)  on  the  19th 
of  April ;  Gemini  ( JC)  on  the  20th  of  May ;  Cancer  (@)  on 
the  21st  of  June  ;  Leo  (<Q)  on  the  22d  of  July  ;  and  Virgo(\tt>) 
on  the  22d  of  August. 

The  foregoing  are  called  northern  signs,  because  the  sun 
must  have  north  declination  while  the  sun  is  in  them. 

The  following  are  designated  as  the  southern  signs  of  the 

Does  the  ecliptic  intersect  the  equator  ?  At  what  angle  ?  "What  point 
in  the  heavens  is  called  the  Vernal  Equinoz  ?  What  is  the  Zodiac  ?  What 
is  meant  by  the  signs  of  the  Zodiac  ?  When  does  the  sun  enter  the  first 
sign  of  the  Zodiac  ? 


INTRODUCTION'.  17 

zodiac,  because  the  sun  must  have  south  declination  while  he 
is  in  them : 

The  sun  enters  Libra  (LTU)  on  the  23d  of  September;  Scorpio 
(If)  )  on  the  22d  of  October  ;  Sagittarius  (^()  on  the  22d  of 
November  ;  Capricornus  (/§)  on  the  21st  of  December  ;  Aqua- 
rius (*»)  on  the  20th  of  January ;  and  Pisces  (^()  on  the  19th 
of  February.  Passing  through  this  last  sign  the  sun  again 
enters  (°p)  on  the  20th  of  March,  to  perform  the  revolution 
over  again,  and  thus  it  goes  on  year  by  year. 

The  zodiac  and  signs  of  the  zodiac  being  but  the  offspring 
of  astrology  and  heathen  mythology,  they  are  entirely  dis- 
carded by  modern  astronomers  ;  yet  they  still  linger  in  country 
almanacs  and  in  many  school  books,  and  it  is  with  reluctance 
that  we  even  mention  them.  They  are  of  no  use,  even  as 
points  of  reference,  and  they  embrace  no  scientific  principle 
whatever. 

Conjunction. — When  two  celestial  bodies  have  the  same  lon- 
gitude, they  are  said  to  be  in  conjunction. 

When  two  celestial  bodies  have  the  same  right  ascension,  that 
is,  come  to  the  meridian  at  the  same  time,  they  are  said  to  be  in 
conjunction  in  right  ascension. 

Opposition. — When  two  celestial  bodies  have  a  difference  of 
longitude  of  180  degrees,  they  are  said  to  be  in  opposition. 

Direct. — Direct,  in  astronomy,  is  a  motion  to  the  eastward 
among  the  stars. 

Retrograde. — Retrograde  is  a  motion  to  the  westward  among 
the  stars.  Stationary  means  apparently  so  in  respect  to  the 
stars.  Other  terms  not  here  mentioned  will  be  explained  as 
we  use  them. 

Why  are  some  of  the  signs  called  northern,  and  others  southern  signs  ? 
Is  the  distinction  of  signs  necessary  ?  What  is  meant  by  conjunction  ? 
By  opposition  ?  What  by  direct  ?  Retrograde  ? 

2 


18  ELEMENTARY  ASTRONOMY. 

CHAPTER   II. 
PRELIMINARY   OBSERVATIONS. 

To  commence  the  study  of  astronomy,  we  must  observe  and 
call  to  mind  the  real  appearance  of  the  heavens. 

Take  such  a  station,  any  clear  night,  as  will  command  an 
extensive  view  of  that  apparent,  concave  hemisphere  above  us, 
which  we  call  the  sky,  and  fix  well  in  the  mind  the  directions 
of  north,  south,  east,  and  west. 

At  first,  let  us  suppose  the  observer  to  be  somewhere  in  the 
United  States,  or  somewhere  in  the  northern  hemisphere,  about 
40  degrees  from  the  equator. 

Soon  he  will  perceive  a  variation  in  the  position  of  the 
stars :  those  at  the  east  of  him  will  apparently  rise ;  those  at 
the  west  will  appear  to  sink  lower,  or  fall  below  the  horizon ; 
those  at  the  south,  and  near  his  zenith,  will  apparently  move 
westward ;  and  those  at  the  north  of  him,  which  he  may  see 
about  half  way  between  the  horizon  and  the  zenith,  will  appear 
stationary. 

Let  such  observations  be  continued  during  all  the  hours  of 
the  night,  and  for  several  nights,  and  the  observer  cannot  fail 
to  be  convinced  that  not  only  all  the  stars,  but  the  sun,  moon, 
and  planets,  appear  to  perform  revolutions,  in  about  twenty- 
four  hours,  round  a  fixed  point;  and  that  fixed  point,  as  ap- 
pears to  us  (in  the  middle  and  northern  part  of  the  United 
States),  is  about  midway  between  the  northern  horizon  and 
the  zenith. 

It  should  always  be  borne   in  mind  that  these  motions  are 

How  can  a  person  convince  himself  that  some  of  the  stars  have  an  appa- 
rent motion  from  east  to  west,  like  the  sun  in  the  day  time  ?  Do  all  the 
stars  have  such  an  apparent  motion,  as  seen  from  this  place  ?  What  stars 
do  not? 


PRELIMINARY  OBSERVATIONS.  19 

but  apparent,  the  stars  keeping  the  same  positions  with  respect 
to  each  other,  whether  they  are  rising  or  falling,  or  north  or 
south  of  the  observer,  and  the  general  aspect  of  the  heavens  is 
the  same  now,  as  it  was  in  the  very  earliest  ages  of  astronomy, 
and  will  be  the  same  in  ages  to  come. 

All  the  heavenly  bodies,  whether  sun,  moon,  planets,  or 
stars,  appear  to  have  a  diurnal  motion  round  a  fixed  point,  and 
all  those  stars  which  are  90  degrees  from  that  point,  appa- 
rently describe  a  great  circle.  Those  stars  which  are  nearer 
to  the  fixed  point  than  90  degrees,  describe  smaller  circles;  and 
the  circles  are  smaller  and  smaller  as  the  objects  are  nearer 
and  nearer  infixed  point. 

There  is  one  star  so  near  this  fixed  point,  that  the  small  cir- 
cle, it  describes,  in  about  24  hours,  is  not  apparent  from  mere 
inspection.  To  detect  the  apparent  motion  of  this  star,  we 
must  resort  to  nice  observations,  aided  by  mathematical  in- 
struments. 

This  fixed  point,  that  we  have  several  times  mentioned,  is  the 
North  Pole  of  the  heavens,  and  this  one  star  that  we  have  just 
mentioned,  is  commonly  called  the  North  Star,  or  the  Pole 
Star. 

As  the  North  Star  appears  stationary,  to  the  common  ob- 
server, it  has  always  been  taken  as  the  infallible  guide  to 
direction;  and  every  sailor  of  the  ocean,  and  every  wanderer 
of  the  African  and  Arabian  deserts,  has  held  familiar  acquain- 
tance with  it. 

If  our  observer  now  goes  more  to  the  southward,  and  makes 
the  same  observations  on  the  apparent  motions  of  the  stars,  he 
will  find  the  same  general  results ;  each  individual  star  will 
describe  the  same  circle  ;  but  the  pole,  the  fixed  point,  will  be 
lower  down,  and  nearer  to  the  northern  horizon  ;  and  it  will  be 

Those  stars  that  do  not  rise  and  set,  what  motion,  real  or  apparent,  do 
they  have  ?  Is  any  star  apparently  stationery  ?  Is  there  a  star  just  at  the 
north  pole  ?  What  use  has  been  made  of  the  north  star  ?  If  a  person 
should  go  south  from  this  place,  what  apparent  effect  would  that  have  on 
the  north  star,  as  viewed  by  him  ? 


20  ELEMENTARY  ASTRONOMY. 

lower  and  lower  in  proportion  to  the  distance  the  observer  goes 
to  the  south.  After  the  observer  has  gone  sufficiently  far,  the 
fixed  point,  the  pole,  will  no  longer  be  up  in  the  heavens,  but 
down  in  the  northern  horizon  ;  and  when  the  pole  does  appear 
in  the  horizon,  the  observer  is  at  the  equator,  and  from  that 
line  all  the  stars  at  or  near  the  equator  appear  to  rise  up  di- 
rectly from  the  east,  and  go  down  directly  to  the  west ;  and  all 
other  stars,  situated  out  of  the  equator,  describe  their  small 
circles  parallel  to  this  perpendicular  equatorial  circle. 

If  the  observer  goes  south  of  the  equator,  the  north  pole  will 
sink  below  his  horizon,  and  the  south  polar  point  will  appear 
to  rise  up  above  his  horizon,  and  it  will  rise  more  and  more  as 
he  goes  farther  and  farther  south  ;  and  if  he  could  possibly  get 
to  the  south  pole  on  the  earth,  the  south  pole  of  the  apparent 
revolving  heavens  would  be  right  over  his  head,  and  the  equa- 
tor of  the  heavens  would  bound  his  horizon. 

In  a  similar  manner  if  an  observer  goes  north,  the  north  pole 
to  him  would  appear  to  rise  in  the  heavens;  and  should  he  con- 
tinue to  go  north,  he  would  finally  find  the  pole  in  his  zenith, 
and  all  the  stars  would  apparently  make  circles  round  the 
zenith,  as  a  center,  and  parallel  to  the  horizon ;  and  the  horizon 
itself  would  be  the  celestial  equator. 

When  the  north  pole  of  the  heavens  appears  at  the  zenith, 
the  observer  must  then  be  at  the  north  pole,  on  the  earth,  or 
at  the  latitude  of  90  degrees. 

Any  celestial  body,  which  is  north  of  the  equator,  is  always 
visible  from  the  north  pole  of  the  earth  ;  hence,  the  sun,  which 
is  north  of  the  equator  from  the  20th  of  March  to  the  23d  of 
September,  must  be  constantly  visible  during  that  period,  in  a 
clear  sky. 

Just  as  the  sun  comes  north  of  the  equator,  its  diurnal  pro- 
gress, or  rather,  the  progress  of  24  hours,  is  around  the  horizon. 
When  the  sun's  declination  is  10  degrees  north  of  the  equator, 

What  is  the  apparent  diurnal  motion  of  the  stars,  as  seen  from  the  equa- 
tor ?  What  from  the  south  pole  ?  What  part  of  the  heavens  bounds  the 
horizon  as  seen  from  the  south  pole  ?  What  from  the  north  pole  ? 


PRELIMINARY  OBSERVATIONS.  21 

the  progress  of  the  sun,  in  24  hours,  as  seen  from  the  north  pole, 
is  around  the  horizon  at  an  altitude  of  about  10  degrees ;  and 
so  on  for  any  other  degree. 

From  the  north  pole,  all  directions  on  the  surface  of  the  earth 
are  south.  North,  strictly  speaking,  would  be  in  a  vertical 
direction,  which  would  make  the  absolute  south  directly  down 
towards  the  center  of  the  earth. 

We  have  observed  that  the  pole  of  the  heavens  rises  as  we 
go  north,  and  sinks  toward  the  horizon  as  we  go  south ;  and 
when  we  observe  that  the  pole  has  changed  its  position  one 
degree,  in  relation  to  the  horizon,  we  know  that  we  must 
have  changed  place  one  degree  on  the  surface  of  the  earth. 

Now  we  know  by  observation,  that  if  we  go  north  about  69£ 
English  miles  on  the  earth,  the  north  pole  will  be  one  degree 
higher  above  the  horizon.  Therefore  69£  miles  corresponds  to 
one  degree,  on  the  earth ;  and  hence,  the  whole  circumference 
of  the  earth  must  be  69^  multiplied  by  360  :  for  there  are  360 
degrees  to  every  circle.  This  gives  24,930  miles  for  the  cir- 
cumference of  the  earth,  and  7,930  miles  for  its  diameter,  which 
is  not  far  from  the  truth. 

Here,  in  the  United  States,  or  anywhere  either  in  Europe, 
Asia,  or  America,  north  of  the  equator,  say  in  latitude  40  de- 
grees, the  north  pole  of  the  heavens  must  appear  at  an  altitude 
of  40  degrees  above  the  horizon ;  and  as  all  the  stars  and 
heavenly  bodies  apparently  circulate  round  this  point  as  a  center, 
it  follows  that  all  those  stars  which  are  within  40  degrees  of  the 
pole,  can  never  go  below  the  horizon,  but  circulate  round  and 
round  the  pole.  All  those  stars  which  never  go  below  the 
horizon,  are  called  circumpolar  stars. 

At  the  north,  and  very  near  the  north  pole,  the  sun  is  a  cir- 
compolar  body  while  it  is  north  of  the  equator,  and  it  is  a 

Describe  the  apparent  diurnal  motion  of  the  sun  from  the  north  pole 
when  its  declination  is  15  degrees  north  ?  How  far  must  we  go  north  or 
south  on  the  earth  to  change  the  apparent  altitude  of  the  pole  one  degree  ? 
What  does  that  show  ?  What  is  meant  by  circumpolar  stars  ?  Would  the 
term  circumpolar  apply  if  the  observer  were  at  the  equator  ? 


22  ELEMENTARY  ASTRONOMY. 

circumpolar  body  as  seen  from  the  south  pole,  while  it  is  south 
of  the  equator ;  this  gives  six  months  day  and  six  months 
night,  at  the  poles. 

North  of  latitude  66  degrees,  and  when  the  sun's  decima- 
tion is  more  than  23  degrees  north  (as  it  is  on  and  about  the 
20th  of  June  in  each  year),  then  the  sun  comes  at,  or  very 
near,  the  northern  horizon,  at  midnight ;  it  is  nearly  east,  at  6 
o'clock  in  the  morning;  it  is  south,  at  noon,  and  about  46  de- 
grees in  altitude ;  and  is  nearly  west  at  6  in  the  afternoon. 

In  all  latitudes  and  from  all  places  on  the  earth,  the  sun  is 
observed  to  circulate  round  the  nearest  pole,  as  a  center ;  and 
when  the  sun  is  on  the  same  side  of  the  equator  as  the  obser- 
ver, more  than  half  of  the  sun's  diurnal  circle  is  above  the  ho- 
rizon, and  the  observer  will  have  more  than  12  hours  sunlight. 

When  the  sun  is  on  the  equator,  the  horizon,  of  every  lati- 
tude, cuts  the  sun's  diurnal  circle  into  two  equal  parts,  and 
gives  12  hours  day  and  12  hours  night,  the  world  over. 
When  the  sun  is  on  the  opposite  side  of  the  equator  from  the 
observer,  the  smaller  segment  of  the  sun's  diurnal  circle  is 
above  the  horizon,  and,  of  course,  gives  shorter  days  than 
nights. 

We  have,  thus  far,  made  but  rude  and  very  imperfect  ob- 
servations on  the  apparent  motion  of  the  heavenly  bodies,  and 
have  satisfied  ourselves  only  of  two  facts : 

1st.  That  all  the  stars,  sun,  moon,  and  planets,  included, 
apparently  circulate  round  the  pole,  and  round  the  earth,  in  a 
day,  or  in  about  24  hours. 

2d.  That  the  sun  comes  to  the  meridian,  at  different  alti- 
tudes above  the  horizon,  at  different  seasons  of  the  year,  giv- 
ing long  days  in  June,  and  short  days  in  December,  in  all 
northern  latitudes. 

Describe  the  appearance  of  the  sun,  during  24  hours,  as  seen  from 
latitude  66  degrees  north,  when  the  sun's  declination  is  23  degrees  nortl. 
Describe  the  diurnal  appearance  of  the  sun,  as  seen  from  the  north  pole, 
when  the  sun  is  on  the  equator,  when  its  declination  is  13  degrees  ncrth. 
What  two  facts  are  thus  far  established  ? 


PRELIMINARY  OBSERVATIONS.  23 

Let  us  now  pay  attention  to  some  other  particulars.  Let  us 
look  at  tbe  different  groups  of  stars,  and  individual  stars,  so 
that  we  can  recognize  them  night  after  night. 

By  a  little  systematic  observation,  which  we  shall  describe 
a  little  further  on,  or  even  without  any  particular  system  of 
observation,  almost  any  one  is  able  to  recognize  certain  stars, 
or  groups  of  stars,  such  as  the  Seven  Stars,  the  Belt  of  Orion, 
Aldebaran,  Sirius,  and  the  like,  and  having  likewise  the  use  of 
a  clock,  he  can  observe  when  any  particular  star  comes  to  any 
definite  position. 

Let  a  person  place  himself  at  any  particular  point,  to  the 
north  of  any  perpendicular  line,  as  the  edge  of  a  wall  or  build- 
ing, and  let  him  observe  the  stars  as  they  pass  behind  the 
building,  in  their  diurnal  motions  from  the  east  to  the  west. 
For  example,  let  us  suppose  that  the  observer  is  watching  the 
star  Aldebaran,  and  that,  when  the  eye  is  placed  in  a  particu- 
lar definite  position,  the  star  passes  behind  the  building  at 
exactly  8  o'clock. 

The  next  evening,  the  same  star  will  come  to  the  same  point 
about  4  minutes  before  8  o'clock ;  and  it  will  not  come  to  the 
same  point  again,  at  8  o'clock  in  the  evening,  until  after  the 
expiration  of  one  year. 

But  in  any  year,  on  the  same  day  of  the  month,  and  at  the 
same  hour  of  the  day,  the  same  star  will  be  at,  or  very  near, 
the  same  position,  as  seen  from  the  same  point. 

For  instance,  if  certain  stars  come  on  the  meridian  at  a  par- 
ticular time  in  the  evening,  on  the  first  day  of  December,  the 
same  stars  will  not  come  on  the  meridian  again,  at  the  same 
time  of  the  night,  until  the  first  day  of  the  next  December. 

On  the  first  of  January,  certain  stars  come  to  the  meridian 
at  midnight ;  and  (speaking  loosely)  every  first  of  January  the 
same  stars  come  to  the  meridian  at  the  same  time ;  and  there 

Does  the  same  fixed  star  come  to  the  meridian  at  the  same  hour  every 
night  ?  Does  it  come  to  the  meridian  earlier  or  later  ?  If  a  star  come  to 
the  meridian  at  1 0  o'clock  in  the  evening  any  particular  night,  when  will 
it  come  to  the  meridian  again  at  the  same  time  in  the  evening  ? 


24  ELEMENTARY  ASTRONOMY. 

will  be  no  other  day  during  the  whole  year,  when  the  same 
stars  will  come  to  the  meridian  at  midnight. 

Thus,  the  same  day  of  every  year  is  observed  to  have  tho 
same  position  of  the  stars  at  the  same  hour  of  the  night ;  and 
this  is  the  most  definite  index  for  the  expiration  of  a  year. 

The  year  is  also  indicated  by  the  change  of  the  sun's  decli- 
nation, which  the  most  careless  observer  cannot  fail  to  notice. 
On  the  21st  of  June,  the  sun  declines  about  23£  degrees  from 
the  equator  towards  the  north ;  and,  of  course,  to  us  in  the 
northern  hemisphere,  its  meridian  altitude  is  so  much  greater, 
and  the  horizontal  shadows  it  casts  from  the  same  fixed  objects 
will  be  shorter ;  and  the  same  meridian  altitude  and  short 
shadow  will  not  occur  again  until  the  following  June,  or  after 
the  expiration  of  one  year. 

Thus,  we  see,  that  the  time  of  the  stars  coming  on  to  the 
meridian,  and  the  declination  of  the  sun,  have  a  close  corres- 
pondence, in  relation  to  time. 

In  all  our  observations  on  the  stars,  we  notice  that  their 
apparent  relative  situations  are  not  changed  by  their  diurnal 
motions.  In  whatever  parts  of  their  circles  they  are  observed, 
or  at  whatever  hour  of  the  night  they  are  seen,  the  same  con- 
figuration is  recognized,  although  the  same  group,  in  the  dif- 
ferent parts  of  its  course,  will  stand  differently,  in  respect  to 
the  horizon.  For  instance,  a  configuration  of  stars  resembling 
the  letter  A,  when  east  of  the  meridian,  will  resemble  the  let- 
ter V,  when  west  of  the  meridian. 

As  the  stars,  in  general,  do  not  change  their  positions  in 
respect  to  each  other,  they  are  called  faed  stars ;  but  there  are 
a  few  important  stars  that  do  change,  in  respect  to  other  stars  ; 
and  for  that  reason  they  become  especial  objects  of  attention, 
and  form  the  most  interesting  portion  of  astronomy. 

In  the  earliest  ages,  those  stars  that  changed  their  places, 

What  is  the  most  definite  index  of  the  expiration  of  a  year  ?  What 
other  index  is  there  of  the  expiration  of  a  year  ?  Do  the  stars  change  their 
configuration  really  or  apparently  while  performing  their  diurnal  circles  ? 
Explain. 


PRELIMINARY   OBSERVATIONS.  26 

were  called  wandering  stars;  and  they  were  subsequently  found 
to  be  the  planetary  bodies  of  the  solar  system,  like  the  earth 
on  which  we  live  ;  or  rather,  the  earth  on  which  we  live,  after 
strict  investigation,  was  found  to  be  a  planet  belonging  to  that 
class  of  wandering  stars  ;  and  this  striking  fact  gives  to  astron- 
omy much  of  its  sublimity  and  importance.  In  a  subsequent 
part  of  this  work  we  hope  to  be  able  to  explain  to  the  general 
reader  how  science  developed  this  and  other  facts,  but  at  pre~ 
sent  they  must  all  be  taken  on  authority. 

The  fixed  stars  come  to  the  meridian  at  intervals  of  23h.  56m. 
4.09s.  of  mean  soler  time,  and  if  any  star  should  be  observed 
coming  to  the  meridian  at  a  greater  interval  of  time,  then  that 
star  could  not  be  a  fixed  star,  but  a  planet,  or  comet,  whose 
motion  was  then  eastward.  But  if  the  interval  be  less  than 
23h.  56m.  4.09s.,  the  star  is  then  wandering  towards  the  west,  and 
is  said  to  be  retrograding. 

The  planets  of  our  system,  sometimes  wander  eastward  — 
sometimes  westward  —  and  sometimes  they  appear  stationary  ; 
but  the  eastward  motion  prevails,  and  all  the  planets  appear  to 
make  revolutions  round  the  earth  from  west  to  east. 

The  apparent  irregularities  of  their  motions,  are  perfectly 
natural  results,  arising  from  the  motion  of  the  earth  round  the 
sun;  and  these  facts  are  brought  in  to  show  that  the  earth  does 
revolve  round  the  sun,  and  is,  in  fact,  a  planet. 

To  study  astronomy  properly,  it  is  not  sufficient  to  read  it 
off  the  pages  of  a  book ;  we  must  read  it  off  of  the  face  of  the 
sky  ;  and  before  we  can  do  that,  we  must  be  better  acquainted 
with  the  face  of  the  sky  utan  we  are  at  present,  and  that  will 
be  the  object  of  the  following  chapter. 

What  stars  became  objects  of  special  attention  to  the  ancients  ?  Is  tLe 
earth  one  of  a  class  of  stars  ?  Was  this  known  in  an  early  day  ? 


26  ELEMENTARY  ASTRONOMY. 

CHAPTER    III. 

THE  FIXED  STARS  —  AS  CELESTIAL  LOCALITIES 

THE  fixed  stars  are  the  only  landmarks  in  astronomy,  in 
respect  to  both  time  and  space.  They  seem  to  have  been 
thrown  about  in  irregular  and  ill-defined  groups  and  clusters, 
called  constellations.  The  individuals  of  these  groups  and 
clusters  differ  greatly  as  to  brightness,  hue,  and  color ;  but 
they  all  agree  in  one  attribute  — a  high  degree  of  permanence, 
as  to  their  relative  positions  in  the  group ;  and  the  groups  are 
as  permanent  in  respect  to  each  other.  This  has  procured 
them  the  title  of  fixed  stars;  an  expression  which  must  be 
understood  in  a  comparative,  and  not  in  an  absolute,  sense  ; 
for,  after  long  investigation,  it  is  ascertained  that  some  of 
them,  if  not  all,  are  in  motion  ;  although  too  slow  to  be  percep- 
tible, except  by  very  delicate  observations,  continued  through 
a  long  series  of  years. 

The  stars  are  also  divided  into  different  classes,  according  to 
their  degree  of  brilliancy,  called  magnitudes.  There  are  six 
magnitudes,  visible  to  the  naked  eye  ;  and  ten  telescopic  mag- 
nitudes —  in  all,  sixteen. 

The  brightest  are  said  to  be  of  the  first  magnitude  ;  those  less 
bright,  of  the  second  magnitude,  etc.;  the  sixth  magnitude  is 
just  visible  to  the  naked  eye. 

The  stars  are  very  unequally  distributed  among  these  classes; 
nor  do  all  astronomers  agree  as  to  the  number  belonging  t-> 
each ;  for  it  is  impossible  to  tell  where  one  class  ends  and 
another  begins ;  nor  is  it  important,  for  all  this  is  but  a  matter 
of  fancy,  involving  no  principle.  In  the  first  magnitude  there 

"What  are  constellations  ?  In  what  sense  should  we  apply  the  term  fixed 
stars  ?  What  is  meant  by  the  magnitude  of  a  star  ?  How  many  classes 
of  magnitudes  are  there  ?  Can  we  define  where  one  class  of  magnitudes 
begins  or  ends  ? 


THE  FIXED  STARS.  27 

is  really  but  one  star  (Sirius) ;  for  this  is  manifestly  brighter 
than  any  other ;  but  most  astronomers  put  fifteen  or  twenty 
into  this  class. 

The  second  magnitude  includes  from  fifty  to  sixty ;  the  third 
about  two  hundred,  the  numbers  increasing  very  rapidly,  as 
we  descend  in  the  scale  of  brightness. 

From  some  experiments  on  the  intensity  of  light,  it  has  been 
determined,  that  if  we  put  the  light  of  a  star,  of  the  average 
1st  magnitude,  100,  we  shall  have: 

1st  magnitude  =100  4th  magnitude  =  6 

2d         "  =     25  5th         "  =  2 

3d         "  =     12  6th         "  =  1 

On  this  scale,  Sir  William  Herschel  placed  the  brightness  of 

Sirius  at  320. 

Ancient  astronomy  has  come  down  to  us  much  tarnished 
with  superstition  and  heathen  mythology.  Every  constellation 
bears  the  name  of  some  pagan  deity,  and  is  associated  with 
some  absurd  and  ridiculous  fable;  yet,  strange  as  it  may 
appear,  these  masses  of  rubbish  and  ignorance  —  these  clouds 
and  fogs,  intercepting  the  true  light  of  knowledge,  are  still  not 
only  retained,  but  cherished,  in  many  modern  works,  and  dig- 
nified with  the  name  of  astronomy.* 

*  As  a  specimen  of  what  was  once  called  astronomy,  and  is  even  now 
studied  for  astronomy  in  some  female  boarding  schools,  we  give  the  follow- 
ing extracts,  taken  from  Keith  on  the  globes.  To  say  nothing  of  other 
branches  of  knowledge,  we  congratulate  the  learner  that  ancient  fables  no 
longer  obscure  astronomy. 

"  COMA  BERENICES  is  composed  of  the  unformed  stars,  between  the  Lion's 
tail  and  Bootes.  Berenice  was  the  wife  of  Evergetes,  a  surname  signifying 
benefactor  :  when  he  went  on  a  dangerous  expedition,  she  vowed  to  dedi- 
cate her  hair  to  the  goddess  Venus,  if  he  returned  in  safety.  Sometime 
after  the  victorious  return  of  Evergetes,  the  locks  which  were  in  the  temple 
of  Venus,  disappeared  ;  and  Conon,  an  astronomer,  publicly  reported  that 
Jupiter  had  carried  them  away,  and  made  them  a  constellation. 

"  COR.  CAROLI,  or  Charles's  heart,  in  the  neck  of  Chara,  the  southernmost 
of  the  two  dogs  held  in  a  string  by  Bootes,  was  so"  denominated  by  Sir 
Charles  Scarborough,  physician  to  king  Charles  II,  in  honor  of  King 
Charles  I." 

How  many  stars  are  there  in  the  first  magnitude  ?  What  is  said  of  ar 
cieut  superstition,  and  mythology  ? 


28  ELEMENTAKY  ASTRONOMY. 

Merely  as  names,  either  to  constellations  or  to  individual 
stars,  we  shall  make  no  objections ;  and  it  would  be  useless,  if 
we  did ;  for  names  long  known,  will  be  retained,  however  im- 
proper or  objectionable ;  hence,  when  we  speak  of  Orion,  the 
Little  Dog,  or  the  Great  Bear,  it  must  not  be  understood  that 
we  have  any  great  respect  for  mythology. 

It  is  not  our  object  now  to  give  any  very  minute  or  scien- 
tific description  of  the  starry  heavens  —  such  as  pointing  out 
the  variable,  double,  and  multiple  stars  —  the  Milky  Way,  and 
nebulce;  these  will  receive  special  attention  in  somo  future 
chapter :  at  present,  our  only  aim  is  to  point  out  the  method  of 
obtaining  a  knowledge  of  the  mere  appearance  of  the  sky,  to 
the  common  observer,  which  may  be  called  the  geography  of 
the  heavens. 

To  give  a  person  an  idea  of  locality,  on  the  earth,  we  refer 
to  points  and  places  supposed  to  be  known.  Thus,  when  we 
say  that  a  certain  town  is  15  miles  northwest  of  Boston,  or 
that  a  ship  is  100  miles  east  of  the  Cape  of  Good  Hope,  or 
that  a  certain  mountain  is  10  miles  north  of  Calcutta,  we  have 
a  pretty  definite  idea  of  the  locality  of  the  town,  the  ship,  and 
the  mountain,  on  the  face  of  the  earth,  provided  we  have  a 
clear  idea  of  the  face  of  the  earth,  and  know  the  position  of 
Boston,  the  Cape  of  Good  Hope,  and  Calcutta. 

So  it  is  with  the  geography  of  the  heavens ;  the  apparent 
surface  of  the  whole  heavens  must  be  in  the  mind,  and  then 
the  localities  of  certain  bright  stars  must  be  known,  as  land- 
marks, like  Boston,  the  Cape  of  Good  Hope,  and  Calcutta. 

We  shall  now  make  some  effort  to  point  out  these  landmarks. 
The  North  Star  is  the  first,  and  most  important  to  be  recog- 
nized ;  and  it  can  always  be  known  to  an  observer,  in  any 
northern  latitude,  from  its  stationary  appearance  and  altitude  ; 
which  is  never  more  than  one  and  a  half  degrees  from  the  lati- 
tude of  the  observer.  Thus,  a  person  in  10°  north  latitude, 

How  does  the  author  regard  mythology?  What  is  meant  by  the 
geography  of  the  heavens?  What  star  is  the  most  important  to  be  recog- 
nized ?  How  can  it  be  kuowu  ? 


THE  FIXED   STARS. 


29 


will  find  the  north  star  very  nearly  in  a  northern  direction, 
between  8°  and  12°  above  the  northern  horizon.  An  observer 
in  25°  north  latitude,  will  find  the  north  star  nearly  north  in 
direction,  and  between  24°  and  26°  of  altitude,  and  so  on  for 
any  other  northern  latitude.  It  is  by  such  observations  on  the 
north  star,  that  latitude  can  be  found. 

When  the  influence  of  refraction  is  allowed  for,  the  latitude  of  a 
place  is  midway  between  the  greatest  and  least  altitudes  of  the  north 
star. 


We  have  here  attempted  to  make  a  faint  representation  of  the 
region  about  the  north  pole  to  the  distance  of  40°.  The  hours 
are  hours  of  right  ascension  in  the  heavens.  -  The  pole  star  is 
nearly  (not  exactly)  in  the  center  of  this  circle.  Directly 

What  star  is  always  very  nearly  north?  What  is  the  latitude  of  any 
place  in  the  northern  hemisphere  equal  to? 


SO  ELEMENTARY  ASTRONOMY. 

opposite  the  cup  or  Great  Bear,  is  the  constellation  Cassiopea. 
E  is  the  position  of  the  pole  of  the  ecliptic,  and  a  little  south 
of  E,  in  right  ascension,  about  18  hours,  is  the  constellation 
called  the  Dragon  or  Draco.  At  the  distance  of  about  32  de- 
grees from  the  pole,  are  seven  bright  stars,  between  the  1st 
and  2d  magnitudes,  forming  a  figure  resembling  a  dipper,  four 
of  them  forming  the  cup,  and  three  the  handle.  They  occupy 
a  space  between  the  right  ascension  of  lOh.  45m.  and  13h.  40m. 
The  two  stars  forming  the  sides  of  the  cup,  opposite  to  the  han- 
dle, are  always  in  a  line  with  the  North  Star,  and  are  therefore 
called  pointers :  they  always  point  to  the  North  Star.  The  line 
joining  the  equinoxes,  or  the  first  meridian  of  right  ascension, 
runs  from  the  pole,  between  the  other  two  stars  forming  the 
cup.  The  first  star  in  the  handle,  nearest  the  cup,  is  called 
Alloth,  the  next  Mizar,  near  which  is  a  small  star,  of  the  4th 
magnitude ;  the  last  one  is  Benetnasch.  The  stars  in  the  han- 
dle are  said  to  be  in  the  tail  of  the  Great  Bear. 

About  four  degrees  from  the  pole  star,  is  a  star  of  the  3d 
magnitude,  S  Ursce  Minoris.  A  line  drawn  through  the  pole 
(not  pole  star)  and  this  star,  will  pass  through,  or  very  near, 
the  poles  of  the  ecliptic  and  the  tropics.  A  small  constellation, 
near  the  pole,  is  called  Ursa  Minor,  or  the  Little  Bear.  An 
irregular  semicircle  of  bright  stars,  between  the  dipper  and 
the  pole,  is  called  the  Serpent. 

If  a  line  be  drawn  from  £  Ursce  Minoris,  through  the  pole 
star,  and  continued  about  45  degrees,  it  will  strike  a  very  beau- 
tiful star,  of  the  1st  magnitude,  called  Capetta.  Within  five 
degrees  of  Capella  are  three  stars,  of  about  the  4th  magnitude, 
forming  a  very  exact  isosceles  triangle,  the  vertical  angle  about 
28  degrees.  A  line  drawn  from  Alioth,  through  the  pole  star, 
and  continued  about  the  same  distance  on  the  other  side,  passes 
through  a  cluster  of  stars  called  Cassiopea  in  her  chair.  The 

Why  are  two  certain  stars  called  pointers  V  What  small  constellation 
is  near  the  north  pole  ?  What  stars  are  in  the  handle  of  the  cup,  or  in  the 
tail  of  the  Great  Bear  ? 


THE  FIXED  STARS.  31 

principal  star  in  Cassiopea,  with  the  pole  star  and  Capella,  form 
an  isosceles  triangle,  Capella  at  the  vertex. 

More  attention  has  been  paid  to  the  constellations  along  the 
equator  and  ecliptic,  than  to  others  in  remoter  regions  of  the 
heavens,  because  the  sun,  moon,  and  planets,  apparently  traverse 
through  them. 

There  are  nine  bright  stars  near  the  ecliptic,  which  are  used 
by  seamen,  in  connection  with  the  position  of  the  moon,  to  find 
longitude  from, — and  for  this  reason  these  stars  are  called  lunar 
stars.  Their  proper  names  are  Arietis,  Aldebaran,  Pollux,  Reg- 
ulus,  Spica,  Antares,  Aquilce,  Fomalhaut,  and  Pegasi. 

Beginning  with  the  first  point  of  Aries  as  it  now  stands,  no 
prominent  stars  are  near  it ;  and,  going  along  the  ecliptic  to  the 
eastward,  there  is  nothing  to  arrest  special  attention,  until  we 
come  to  the  Pleiades,  or  Seven  Stars,  though  only  six  are  visible 
to  the  naked  eye.  This  little  cluster  is  so  well  known,  and  so 
remarkable,  that  it  needs  no  description.  Southeast  of  the 
Seven  Stars,  at  the  distance  of  about  18  degrees,  is  a  remark- 
able cluster  of  stars,  said  to  be  in  the  Bull's  Head ;  the  largest 
star  in  this  cluster  is  of  the  1st  magnitude,  of  a  red  color, 
called  Aldebaran.  It  is  one  of  the  nine  stars  selected  as  points 
from  which  to  compute  the  moon's  distance,  for  the  assistance 
of  navigators. 

This  cluster  resembles  an  A  when  east  of  the  meridian,  and 
a  V  when  west  of  it.  The  Seven  Stars,  Aldebaran,  and  Capella, 
form  a  triangle  very  nearly  isosceles  —  Capella  at  the  vertex. 
A  line  drawn  from  the  Seven  Stars,  a  little  to  the  west  of  Alde- 
baran, will  strike  the  most  remarkable  constellation  in  the 
heavens,  Orion,  (it  is  out  of  the  zodiac  however)  ;  some  call  it 
the  Ell  and  Yard.  The  figure  is  mainly  distinguished  by  three 
stars  in  one  direction,  within  two  degrees  of  each  other  ;  and 
two  other  stars,  forming,  with  one  of  the  three  first  mentioned, 
another  line  at  right  angles  with  the  first  line. 

Why  are  certain  stars  called  lunar  stars  ?  Is  there  any  star  near  the  first 
point  of  Aries  ?  What  is  meant  by  the  first  point  of  Aries  ?  What  bright 
star  is  about  18°  southeast  of  the  Seven  Stars  ?  How  would  you  find  Orion 
on  seeing  the  Seven  Stars  and  Aldebaran  ? 


32  ELEMENTARY  ASTRONOMY. 

The  five  stars  thus  in  lines,  are  of  the  1st  or  2d  magnitude. 
A  line  from  the  Seven  Stars,  passing  near  Aldebaran  and  through 
Orion,  will  pass  very  near  to  Sirius,  the  most  brilliant  star  in 
the  heavens.  The  ecliptic  passes  about  midway  between  the 
Seven  Stars  and  Aldebaran,  in  nearly  an  eastern  direction. 
Nearly  due  east  from  the  northernmost  and  brightest  star  in 
Orion,  and  at  the  distance  of  about  25  degrees,  is  the  stai 
Procyon  ;  a  bright,  lone  star. 

The  northernmost  star  in  Orion,  with  Sirius  and  Procyon, 
form  an  equilateral  triangle. 

Directly  north  of  Procyon,  at  the  distances  of  25  or  30 
degrees,  are  two  bright  stars,  Castor  and  Pollux.  Castor  is 
the  most  northern.  Pollux  is  one  of  the  nine  lunar  stars. 
Thus  we  might  run  over  that  portion  of  the  heavens  which  is 
ever  visible  to  us,  and  by  this  method  every  student  of  astro- 
nomy can  render  himself  familiar  with  the  aspect  of  the  sky ; 
but  it  is  not  sufficiently  definite  and  scientific  to  satisfy  a  ma- 
thematical mind. 

The  only  scientific  method  of  defining  the  position  of  a  place 
on  the  earth,  is  to  mention  its  latitude  and  longitude;  and  this 
method  fully  defines  any  and  every  place,  however  unimpor- 
tant and  unfrequented  it  may  be :  so  in  astronomy,  the  only 
scientific  method  of  defining  the  position  of  a  star,  is  to  men- 
tion its  latitude  and  longitude,  or,  more  conveniently,  its  riyld 
ascension  and  declination. 

It  is  not  sufficient  to  tell  the  navigator  that  a  coast  makes 
off  in  such  a  direction  from  a  certain  point,  and  that  it  is  so 
far  to  a  certain  cape  ;  and,  from  one  cape  to  another,  it  is  about 
40  miles  south-west — he  would  place  very  little  reliance  on 
any  such  directions.  To  secure  his  respect,  and  command  hi& 
confidence,  the  latitude  and  longitude  of  every  point,  promon- 
tory, river,  and  harbor,  along  the  coast,  must  be  given ;  and 
then  he  can  shape  his  course  to  any  point,  or  strike  in  upon  it 

What  three  bright  stars  form  an  equilateral  triangle  ?  Where  is  Castor 
and  Pollux  ?  What  is  the  scientific  method  of  defining  a  place  on  the 
earth  ?  What  of  locating  a  star  in  the  heavens  ? 


THE  FIXED  STARS.  33 

from  the  indefinite  expanse  of  a  pathless  sea.  So  with  an 
astronomer ;  while  he  understands  and  appreciates  the  rough 
aud  general  descriptions,  such  as  we  have  just  given,  he  re- 
quires the  certain  description,  comprised  in  right  ascension  and 
declination. . 

Accordingly,  astronomers  have  given  the  right  ascensions 
and  declinations  of  every  visible  star  in  the  heavens  (and  of 
very  many  that  are  invisible),  and  arranged  them  in  tables, 
in  the  order  of  right  ascension. 

There  are  far  too  many  stars,  for  each  to  have  a  proper 
name ;  and,  for  the  sake  of  reference,  Mr.  John  Bayer,  of 
Augsburg,  in  Suabia,  about  the  year  1603,  proposed  to  denote 
the  stars  by  the  letters  of  the  Greek  and  Roman  alphabets ; 
by  placing  the  first  Greek  letter  a  to  the  principal  star  in  the 
constellation,  /?  to  the  second  in  magnitude,  /to  the  third,  and 
so  on  ;  and  if  the  Greek  alphabet  shall  become  exhausted,  then 
begin  with  the  Roman,  a,  b,  c,  etc. 

"  Catalogues  of  particular  stars,  in  sections  of  the  heavens, 
have  been  published  by  different  astronomers,  each  author 
numbering  the  individual  stars  embraced  in  his  list,  according 
to  the  places  they  respectively  occupy  in  the  catalogue." 
These  references  to  particular  catalogues  are  sometimes  marked 
on  celestial  globes,  thus :  79  H,  meaning  that  the  star  is  the 
79th  in  HerschePs  catalogue ;  37  M,  signifies  the  37th  num- 
ber in  the  catalogue  of  Mayer,  etc. 

Among  our  tables  will  be  found  a  catalogue  of  a  hundred  of 
the  prii  cipal  stars,  inserted  for  the  purpose  of  teaching  a  definite 
and  sci  ntific  method  of  making  a  learner  acquainted  with  the 
geograp  ly  of  the  heavens,  which  will  be  given  in  another  chapter. 

What  did  John  Bayer  propose  ?  How  are  stars,  in  sectional  catalogues, 
referm  to? 


34  ELEMENTARY  ASTRONOMY. 

CHAPTER   IV. 

TIME  — AND  THE  MEASURE  OF  TIME. 

TIME  is  but  a  measured  portion  of  unlimited  duration — and 
it  is  measured  off,  directly  or  indirectly^  by  astronomical  events. 

The  most  obvious  astronomical  event  is  that  of  a  natural  day, 
from  sunrise  to  sunset,  or  from  sunrise  to  sunrise  again,  —  but 
as  these  intervals  are  variable  in  length,  they  are  not  proper 
standards  for  time. 

The  interval  embracing  the  four  seasons  of  the  year,  is 
another  astronomical  period  which  serves  to  measure  time  on 
a  large  and  indefinite  scale. 

The  interval  from  full  moon  to  full  moon  again,  is  also  an 
astronomical  period,  —  but  after  careful  observation,  it  has 
been  found  to  be  a  period  of  variable  duration  ;  and,  moreover, 
it  is  impossible  for  the  unlearned  to  define  the  moment  when 
such  an  interval  begins  or  ends,  — therefore  this  period  is  use- 
less, as  a  measure  of  time  —  and  none  but  savages  pretend  to 
use  it  as  such. 

For  a  standard  of  measure,  we  must  find,  if  possible,  some 
invariable  period  that  can  be  distinctly  defined.  In  the  early 
ages  of  astronomy,  the  interval  from  noon,  to  noon  again,  was 
considered  a  constant  interval,  and  taken  for  the  measure  of 
time,  —  and  for  the  common  business  of  the  world,  this  will 
be  the  standard  for  time,  because  it  is  the  most  obvious,  natu- 
ral, and  convenient.  But  after  close  investigation  and  careful 
observations,  this  interval  was  found  to  be  slightly  variable, 
and  another  interval,  the  passage  of  a  fixed  star  from  the  meri- 
dian to  the  meridian  again,  was  found  to  be  a  constant  interval, 
therefore  this  interval  is  taken  a*  the  standard  measure  of  time. 

What  is  time  ?  What  is  an  astronomical  event  ?  Is  from  noon  to  noon, 
by  the  sun,  an  invariable  interval  of  time?  What  astronomical  events 
mark  equal  intervals  of  time  ? 


TIME— AND  THE  MEASURE  OF  TIME.  35 

The  interval  from  one  passage  of  a  star  across  the  meridian, 
to  the  next,  is  a  sidereal  day,  and  measured  by  the  common 
solar  clock,  the  interval  is  23h.  56m.  4.09s.  No  matter  what 
star  is  observed,  the  interval  is  the  same,  and  as  this  has  been 
the  universal  experience  of  astronomers  in  all  ages,  it  com- 
pletely establishes  the  fact,  that  all  the  fixed  stars  come  to  the 
meridian  in  exactly  equal  intervals  of  time ;  and  this  gives  us 
a  standard  measure  for  time,  and  the  only  standard  measure, 
for  all  other  motions  are  variable  and  unequal. 

Again,  this  interval  must  be  the  time  that  the  earth  employs 
in  turning  on  its  axis ;  for  if  the  star  is  fixed,  it  is  a  mark  for 
the  time,  that  the  meridian  is  in  exactly  the  same  position  in 
relation  to  absolute  space. 

Soon  after  the  fact  was  established  that  the  fixed  stars  came 
to  the  meridian  in  equal  times,  and  that  interval  less  than  24 
hours,  astronomers  conceived  the  idea  of  graduating  a  clock  to 
that  interval,  and  dividing  it  into  24  hours.  Thus  graduating 
a  clock  to  the  stars,  and  not  to  the  sun,  it  is  therefore  called  a 
sidereal,  and  not  a  solar,  or  common  clock ;  and  as  it  was  sug- 
gested by  astronomers,  and  used  only  for  the  purposes  of 
astronomy,  it  is  also  very  appropriately  called  an  astronomical 
clock ;  but  save  its  graduation,  and  the  nicety  of  its  construc- 
tion, it  does  not  differ  from  a  common  clock. 

With  a  perfect  astronomical  clock,  the  same  star  will  pass  the 
meridian  at  exactly  the  same  time,  from  one  year's  end  to  another. 
If  the  time  is  not  the  same,  the  clock  does  not  run  to  sidereal 
time ;  and  the  variation  of  time,  or  the  difference  between 
the  time  when  the  star  passes  the  meridian,  and  the  time 
which  ought  to  be  shown  by  the  clock,  will  determine  the  rate 
of  the  clock.  And  with  the  rate  of  the  clock,  and  its  error,  we 
can  readily  deduce  the  true  time  from  the  time  shown  by  the 
face  of  the  clock.  We  have  several  times  mentioned  the  fact, 
that  the  same  star  returns  to  the  same  meridian  again  and 

What  is  a  sidereal  day  ?  What  is  an  astronomical  clock  ?  How  does 
it  differ  from  a  common  clock  ?  How  can  we  determine  whether  the  as- 
tronomical clock  moves  perfectly  or  not  ? 


36  ELEMENTARY  ASTRONOMY. 

again,  after  every  interval  of  24  sidereal  hours.  So,  two  differ* 
ent  stars  come  to  the  meridian  at  constant  and  invariable 
intervals  of  time  from  each  other;  and  by  such  intervals  wo 
decide  how  far,  or  how  many  degrees,  one  star  is  east  or  west 
of  another.  For  instance,  if  a  certain  fixed  star  was  observed 
to  pass  the  meridian  when  the  sidereal  clock  marked  8  hours, 
and  another  star  was  observed  to  pass  at  9,  just  one  sidereal 
hour  after,  then  we  know  that  the  latter  star  is  on  a  celestial 
meridian,  just  15  degrees  eastward  of  the  meridian  of  the  first 
mentioned  star. 

With  a  perfect  astronomical  clock,  or  one  which  shows  true 
sidereal  time,  we  can  find  the  right  ascension  of  any  heavenly 
body,  by  simply  observing  the  time  it  passes  the  meridian. 
For  right  ascension  is  but  another  term  for  the  sidereal  time  the 
6ody  passes  the  meridian. 

That  meridian  in  the  heavens  which  passes  through  the  point 
where  the  ecliptic  and  equator  intersect,  at  the  first  point  of 
Aries,  the  point  where  the  sun  crosses  the  equator  in  the  spring, 
is  taken  as  the  first  meridian  of  right  ascension,  and  from  thence 
we  reckon  eastward,  from  0  hours  to  24  hours,  to  the  same 
meridian  again. 

This  being  the  case,  the  sidereal  clock  should  show  Oh.  Om. 
Os.  when  the  equinox  is  on  the  meridian  ;  and,  if  a  star  or  a 
planet  were  observed  to  pass  the  meridian  at  4h.  20m  30s., 
then  the  right  ascension  of  that  star  or  planet,  at  that  time, 
was  4h.  20m.  30s. 

This,  however,  is  on  the  supposition  that  the  clock  is  perfect, 
and  runs  perfectly  uniform,  which  is  never  the  case ;  unfor- 
tunately, there  is  no  such  thing  as  a  perfect  clock,  and  the 
difficulties  thus  arising,  must  be  surmounted  by  artifice  and 
multiplied  observations. 

Just  as  the  sun  crosses  the  equator  in  the  spring,  its  right 

How  can  we  find  the  rate  of  the  clock  ?  What  difference  is  there  be- 
tween true  sidereal  time  and  right  ascension  ?  Define  the  first  astronom- 
ical meridian  ?  What  time  should  the  clock  show  when  the  equinox  is  on 
the  meridian  ? 


TIME  — AND   THE  MEASURE  OF  TIME.  37 

ascension  is  Oh.,  and  from  this,  its  right  ascension  increases 
about  four  minutes  each  day  ;  this  shows  that  the  sun  has  an 
apparent  motion  eastward,  among  the  stars. 

The  right  ascensions  of  all  the  fixed  stars  increase  at  a  very 
slow  rate,  in  consequence  of  the  precession  of  the  equinoxes,  that 
is,  a  slow  motion  of  the  first  meridian  to  the  westward,  among 
the  stars,  of  about  50"!  per  year ;  this  gives  the  stars  the  appear- 
ance of  moving  eastward  and  increasing  their  right  ascensions. 
The  entire  increase  since  the  first  reliable  observations  on 
record,  is  about  30°,  or  2  hours. 

The  great  multitude  of  stars  retain  the  same  relative  right 
ascensions,  and  the  same  relative  declinations,  for  very  long 
periods  of  time,  —  that  is,  they  retain  the  same  positions  with 
respect  to  each  other.  But  occasionally,  stars  may  be  observed 
that  change  their  right  ascension  from  day  to  day,  and  these 
stars,  in  early  times,  were  called  wandering  stars  —  mentioned 
in  the  preceding  chapter,  — they  are  the  planets  of  our  system, 
the  earth  itself  being  one  of  them. 

When  it  is  discovered  that  a  star  does  not  pass  the  meridian 
at  equal  intervals  of  time,  as  shown  by  a  good  astronomical 
clock,  we  then  decide  that  that  star  must  have  a  motion  of  its 
own  —  and  of  course  must  be  a  planet  or  a  comet. 

The  reason  why  astronomers  commence  the  day  at  noon 
rather  than  at  midnight,  is  because  noon,  the  time  that  the  sun 
passes  the  meridian,  is  a  distinct  and  visible  moment,  which,  with 
proper  care  and  proper  instruments,  can  be  exactly  defined  by 
observation  ;  not  so  with  midnight,  or  any  other  moment,  du- 
ring the  24  hours. 

Suppose  the  right  ascension  of  a  star  is  8h.  32m.  16s.,  what  time  should 
be  shown  by  the  astronomical  clock,  when  that  star  passes  the  meridian  ? 
How  are  planets  and  comets  distinguished  from  the  fixed  stars?  By  what 
observations?  Why  do  astronomers  commence  the  day  at  noon  ? 


38  ELEMENTARY  ASTRONOMY. 


CHAPTER    V. 

LATITUDE  — DECLINATION  — ASTRONOMICAL 
INSTRUMENTS. 

IN  the  ast  chapter  we  have  given  a  general  idea  of  finding 
the  right  ascensions  of  the  heavenly  bodies —  but  to  give  a  true 
view  or  map  of  the  heavens,  we  must  give  the  declinations  also. 

To  observe  declination,  we  must  have  an  instrument  to 
measure  angles,  and  with  it,  determine  the  latitude  of  the 
place  from  whence  the  observations  are  made. 

The  true  altitude  of  the  celestial  pole  is  the  latitude  of  the  place 
of  observation,  and  primarily,  the  observation  to  find  this  alti- 
tude is  the  only  method  of  finding  the  latitude,  —  but  after  the 
positions  of  the  heavenly  bodies  have  been  established,  then 
there  are  many  other  methods  of  finding  the  latitude. 

As  the  north  pole  is  but  an  imaginary  point,  no  star  being 
there,  we  cannot  directly  observe  its  altitude.  But  there  is  a 
bright  star  near  the  pole,  called  the  Polar  Star,  which,  like 
all  other  stars  in  the  same  region,  apparently  revolves  round 
the  pole,  and  comes  to  the  meridian  twice  in  24  sidereal  hours  ; 
once  above  the  pole,  and  once  below  it ;  and  it  is  evident  that 
the  altitude  of  the  pole  itself  must  be  midway  between  the 
greatest  and  least  altitudes  of  the  same  star,  provided  the  appa* 
rent  motion  of  the  star  round  the  pole  is  really  in  a  circle;  but 
before  we  examine  this  (act,  we  will  show  how  altitudes  can  be 
taken  by  the  mural  circle. 

The  mural,  or  wall  circle,  is  a  large  metalic  circle,  firmly 
fastened  to  a  wall,  so  that  its  plane  shall  coincide  with  the 
plane  of  the  meridian. 

Define  the  latitude  of  a  place.  In  the  early  stages  of  Astronomy,  were 
there  many  ways  of  finding  latitude  ?  When  can  we  find  many  methods 
of  finding  latitude  ?  Is  the  celestial  pole  a  visible  point  ?  How  then  can 
we  define  it  ? 


LATITUDE  —  DECLINATION  —  INSTRUMENTS. 


39 


A  perpendicular  line 
*hrough  the  center,  ZJV, 
represents  the  zenith  and 
nadir  points ;  and  at  right 
angles  to  this,  through  the 
center,  is  the  horizontal 
line,  Hh. 

A  telescope,  Tt,  and  an 
index  bar,  li,  at  right  an- 
gles to  the  telescope,  are 
firmly  fixed  together,  and 
made  to  revolve  on  the 
center  of  the  mural  circle. 

The  circle  is  graduated  from  the  zenith  and  nadir  points, 
each  way,  to  the  horizon,  from  0  to  90  degrees. 

When  the  telescope  is  directed  to  the  horizon,  the  index 
points,  /and  i,  will  be  at  Z  and  ^Y,  and,  of  course,  show  0°  of 
altitude.  When  the  telescope  is  turned  perpendicular  to  Z, 
the  index  bar  will  be  horizontal,  and  indicate  90  degrees  of 
altitude. 

When  the  telescope  is  pointed  toward  any  star,  as  in  the 
figure,  the  index  points,  /and  i,  will  show  the  position  of  the 
telescope,  or  its  angle  from  the  horizon,  which  is  the  altitude  of 
the  star. 

As  the  telescope,  and  index  of  this  instrument,  can  revolve 
freely  round  the  whole  circle,  we  can  measure  altitudes  with 
it  equally  well  from  the  north  or  the  south ;  but  as  it  turns 
only  in  the  plane  of  the  meridian,  we  can  observe  only  meri- 
dian altitudes  with  it. 

This  instrument  has  been  called  a  transit  circle,  and,  says 
Sir  John  Herschel,  "The  mural  circle  is,  in  fact,  at  the  same 
time,  a  transit  instrument ;  and,  if  furnished  with  a  proper  sys- 
tem of  vertical  wires  in  the  focus  of  its  telescope,  may  be  used 
as  such." 


"When  the  telescope  points  to  a  star,  how  will  the  instrument  show  the 
altitude  of  the  star  ?     Can  the  telescope  move  out  of  the  meridian  ? 


40  ELEMENTARY  ASTRONOMY. 

For  a  transit  instrument,  the  focus  of  the  eye-piece  must  be 
furnished  with  a  system  of  wires,  as  here  represented,  "one 
horizontal  and  five  equi-distant  threads  or  wires,  "  which  always 
appear  in  the  field  of  view,  when  properly  illuminated,  by  day 
by  the  light  of  the  sky,  by  night  by  that 
of  a  lamp,  introduced  by  a  contrivance  not 
necessary  here  to  explain.  The  place  of 
this  system  of  wires  may  be  altered  by 
adjusting  screws,  giving  it  a  lateral  (hori- 
zontal) motion;  and  it  is  by  this  moans 
Meridian  Wires,  brought  to  such  a  position,  that  the  middle 
one  of  the  vertical  wires  shall  intersect  the  line  of  collimation 
of  the  telescope,  where  it  is  arrested  and  permanently  fastened. 
In  this  situation  it  is  evident  that  the  middle  thread  will  be  a 
visible  representation  of  that  portion  of  the  celestial  meridian 
to  which  the  telescope  is  pointed;  and  when  a  star  is  seen  to 
cross  this  wire  in  the  telescope,  it  is  in  the  act  of  culminating, 
or  passing  the  celestial  meridian.  The  instant  of  this  event  is 
noted  by  the  clock  or  chronometer,  which  forms  an  indispen- 
sable accompaniment  of  the  transit  instrument.  For  greater 
precision,  the  moment  of  its  crossing  each  of  the  vertical 
threads  is  noted,  and  a  mean  taken,  which  (since  the  threads 
are  equi-distant)  would  give  exactly  the  same  result,  were  all 
the  observations  perfect,  and  will,  of  course,  tend  to  subdivide 
and  destroy  their  errors  in  an  average  of  the  whole." 

To  measure  altitudes  in  all  directions,  we  must  have  another 
instrument,  or  a  modification  of  this. 

Conceive  this  instrument  to  turn  on  a  perpendicular  axis 
parallel  to  ZN,  in  place  of  being  fixed  against  a  wall ;  and 
conceive,  also,  that  the  perpendicular  axis  rests  on  the  center 
of  a  horizontal  circle,  and  on  that  circle  carries  a  horizontal 
index,  to  measure  azimuth  angles. 

This   instrument,    so   modified,    is    called   an  altitude   ana 

How  is  the  meridian  made  visible  ?  "What  is  the  use  of  more  than  one 
verticil  wire?  What  instrument  must  always  accompany  the  transit 
instrument  ?  What  is  meant  by  azimuth  angles  ? 


LATITUDE  —  DECLINATION  —  INSTRUMENTS.  41 

azimuth  instrument,  because  it  can  measure  altitudes  and  azi- 
muths at  the  same  time. 

We  have  before  said,  that  the  altitude  of  the  celestial  pole 
must  be  midway  between  the  greatest  and  least  altitude  of  the 
polar  star,  provided  that  star  apparently  circulates  round  the  pole 
in  a  circle.  To  decide  that  question,  all  we  have  to  do  is  to 
measure  the  direction  of  the  star,  east  and  west  of  the  meridian, 
and  compare  the  amount  with  the  difference  between  its  great- 
est and  least  altitudes,  and  if  the  amount  is  the  same,  the  appa- 
rent motion  is  unquestionably  circular ;  but  observation  shows 
that  the  horizontal  diameter  of  the  circle  is  greater  than  the 
perpendicular  diameter. 

Hence,  we  cannot  say  that  the  midway  altitude  of  the  polar 
star  is  the  measure  of  the  latitude  of  the  place.  But  if  it  is,  the 
same  kind  of  observation  on  other  circumpolar  stars,  must  give 
the  same  latitude.  Such  observations  have  been  taken,  and 
stars  at  the  same  distance  from  the  pole  gave  the  same  lati- 
tude, and  stars  at  different  distances  from  the  pole  gave  differ- 
ent latitudes ;  and  the  greater  the  distance  of  any  star  from  the 
pole,  the  greater  the  latitude  deduced  from  it.  A  star  30  or  35 
degrees  from  the  pole,  observed  from  about  the  latitude  of  40 
degrees,  will  give  the  latitude  12  or  15  minutes  of  a  degree 
greater  than  the  pole  star. 

Astronomers  investigated  this  subject  thoroughly,  and  exam- 
ined the  apparent  paths  of  the  stars  round  the  pole,  by  means 
of  the  altitude  and  azimuth  instrument,  and  they  were  found  to 
be  not  exact  circles;  but  departed  more  and  more  from  a  circle, 
as  the  star  was  a  greater  and  greater  distance  from  the  pole. 

These  curves  were  found  to  be  somewhat  like  ovals  —  the 
longer  diameter  passing  horizontally  through  the  pole  —  the 

What  is  the  latitude  of  a  place  measured  by,  or  what  does  it  correspond 
to  ?  Do  the  stars  apparently  circulate  round  the  pole  in  perfect  circles  ? 
What  kind  of  a  figure  does  the  motion  of  a  star  round  the  pole  appear  to 
describe  ?  What  is  the  position  of  the  longest  diameter  of  these  ovals  ? 
What  half  of  these  ovals  more  nearly  correspond  to  semicircles,  the  upper 
or  lower  V 

4 


42 


ELEMENTARY  ASTRONOMY. 


upper  segments  very  nearly  semicircles,  and  the  lower  segments 
flattened  on  their  under  sides. 

With  such  evidences  before  the  mind,  men  were  not  long 
in  deciding  that  these  discrepancies  were  owing  to 

ATMOSPHERICAL    REFRACTION. 

It  is  shown,  in  every  treatise  on  natural  philosophy,  that 
light,  passing  obliquely  from  a  rarer  medium  into  a  denser,  is 
bent  towards  a  perpendicular  to  the  new  medium. 

Now,  when  rays  of  light  pass,  or  are  conceived  to  pass, 
from  ar^  celestial  objects,  through  the  earth's  atmosphere  to 
an  observer,  the  rays  must  be  bent  downward,  unless  they  pass 
perpendicularly  through  the  atmosphere;  that  is,  come  from 

the  zenith. 

Let    AE,     CD, 

EF,  <fec.  represent 
different  strata  of 
the  earth's  atmos- 
phere. Let  s  be  a 
star,  and  conceive 
a  line  of  light  to 
pass  from  the  star 
through  the  vari- 
ous strata  of  air, 
to  the  observer,  at 
0.  When  the  ray 
of  light  meets  the 
first  strata,  as  EF,  it  is  slightly  bent  downward ;  and  as  the 
air  becomes  more  and  more  dense,  its  refracting  power  be- 
comes greater  and  greater,  which  more  and  more  bends  the 
ray.  But  the  direction  of  the  ray,  at  the  point  where  it  meets 
the  eye  of  the  observer,  will  determine  the  position  of  the  star 
as  seen  by  him.  Hence,  the  observer  at  0  will  see  the  star  at 
*',  when  its  real  position  is  at  s. 

As  a  ray  of  light,  from  any  celestial  object,  is  bent  down- 
Do  lines  of  light  pass  through  the  atmosphere  in  straight  lines  ?    In 
what  direction  are  the  rays  beut  ? 


ATMOSPHERICAL    REFRACTION.  43 

ward,  therefore,  as  we  may  see  by  inspecting  the  figure,  the 
altitude  of  all  the  heavenly  bodies  is  increased  by  refraction. 

This  shows  that  all  altitudes,  as  they  come  from  the  instru- 
ment, must  be  apparent  altitudes  and  not  true  altitudes,  and 
the  apparent  altitude  is  always  greater  than  the  corresponding 
true  altitude,  because  the  body  is  elevated  by  refraction. 

If  it  were  not  for  refraction,  the  curves  round  the  pole 
would  be  perfect  circles,  and  the  mathematician,  by  means  of 
the  altitude  and  azimuth,  which  can  be  taken  at  any  and  every 
point  of  a  curve,  can  determine  how  much  it  deviates  from  a 
circle,  and  from  thence  the  amount  of  refraction,  at  the  several 
points. 

By  using  the  refraction  thus  imperfectly  obtained,  he  can 
correct  his  altitudes,  and  obtain  his  latitude,  to  considerable 
accuracy.  Then,  by  repeating  his  observations,  he  can  fur- 
ther approximate  to  the  refraction. 

In  this  way,  by  a  multitude  of  observations  and  computa- 
tions, the  table  of  refraction  (which  appears  among  the  tables 
of  every  astronomical  work)  was  established  and  drawn  out. 

The  effect  of  refraction,  as  we  have  already  seen,  is  to  in- 
crease the  altitude  of  all  the  heavenly  bodies.  Therefore,  by 
the  aid  of  refraction,  the  sun  rises  before  it  otherwise  would, 
and  does  not  set  as  soon  as  it  would  if  it  were  not  for  refrac- 
tion ;  and  thus  the  apparent  length  of  every  day  is  increased 
by  refraction,  and  more  than  half  of  the  earth's  surface  is  con- 
stantly illuminated.  The  extra  illumination  is  equal  to  a  zone, 
entirely  round  the  earth,  of  about  40  miles  in  breadth. 

As  the  refraction  in  the  horizon  is  about  33'  of  a  degree,  the 
length  of  a  day,  at  the  equator,  is  more  than  four  minutes 
longer  than  it  otherwise  would  be,  and  the  nights  four  minyt.es 
shorter. 

At  all  other  places,  where  the  diurnal  circles  are  oblique  to 

What  is  apparent  altitude  ?  What  is  true  altitude  ?  Which  is  greatest, 
the  apparent  or  the  true  altitude  of  a  heavenly  body  ?  What  effect  does 
refraction  have  on  the  time  of  the  sun's  rising?  What  on  the  length  of  a 
day? 


44  ELEMENTARY  ASTRONOMY. 

the  horizon,  the  difference  is  still  greater,  especially  if  we  take 
the  average  of  the  whole  year. 

In  high  northern  latitudes,  the  long  days  of  summer  are 
very  materially  increased,  in  length,  by  the  effects  of  refrac- 
tion ;  and  near  the  pole,  the  sun  rises,  and  is  kept  above  the 
horizon,  even  for  days,  longer  than  it  otherwise  would  be, 
owing  to  the  same  cause. 

Refraction  varies  very  rapidly,  in  its  amount,  near  the  hori- 
zon ;  and  this  causes  a  visible  distortion  of  both  sun  and  moon, 
just  as  they  rise  or  set. 

For  instance,  when  the  lower  limb  of  the  sun  is  just  in  the 
horizon,  it  is  elevated,  by  refraction,  33'. 

But  the  altitude  of  the  upper  limb  is  then  32',  and  the  re- 
fraction, at  this  altitude,  is  27'  50",  elevating  the  upper  limb 
by  this  quantity.  Hence,  we  perceive,  that  the  lower  limb  is 
elevated  more  than  the  upper ;  and  the  perpendicular  diameter 
of  the  sun  is  apparently  shortened  by  6'  10",  and  the  sun  is 
distinctly  seen  of  an  oval  form,  which  deviates  more  from  a 
circle  below  than  above. 

The  apparently  dilated  size  of  the  sun  and  moon,  when  near 
the  horizon,  has  nothing  to  do  with  refraction  :  it  is  a  mere 
illusion,  and  has  no  reality,  as  may  be  known  by  applying  the 
following  means  of  measurement. 

Roll  up  a  tube  of  paper,  of  such  a  size  and  dimensions  as 
just  to  take  in  the  rising  moon,  at  one  end  of  the  tube,  when 
the  eye  is  at  the  other.  After  the  moon  rises  some  distance 
in  the  sky,  observe  again  with  this  tube,  and  it  will  be  found 
that  the  apparent  size  of  the  moon  will  even  more  than  fill  it. 

When  small  stars  are  near  the  horizon,  they  become  invi- 
sible ;  either  the  refraction  enfeebles  and  dissipates  their  light, 

What  effect  does  refraction  have  on  the  length  of  a  day  in  high  northern 
latitudes  ?  How  much  more  than  half  of  the  earth  is  enlightened  by  the 
sun  at  anyone  time?  What  effect  does  refraction  have  on  the  apparent 
shape  of  the  sun  at  rising  and  setting  ?  Why  should  refraction  give  that 
appearance?  Is  the  moon  apparently  larger  when  near  the  horizon,  than 
when  near  the  zenith  ? 


ATMOSPHERICAL    REFRACTION-  45 

or  the  vapors,  which  are  always  floating  in  the  atmosphere, 
serve  as  a  cloud  to  obscure  them. 

Having  shown  the  possibility  of  making  a  table  of  refraction 
corresponding  to  all  apparant  altitudes,  we  can  now,  by  apply- 
ing its  effects  to  the  observed  altitudes  of  the  circumpolar 
stars,  obtain  the  true  latitude  of  the  place  of  observation. 

A  table  of  refraction  is  to  be  found  in  the  latter  part  of  this 
volume,  and  we  give  a  few  examples  to  explain  its  use. 

1.  The  apparent  altitude  of  a  star  was  31°  20',  what  was  its 
true  altitude? 

By  inspecting  the  table  we  find  1'  35"  corresponds  to  the 
apparent  altitude  31°  20'. 

Therefore,  from         -         -      31°  20'  00" 
Subtract,     ...  1'  35" 


True  altitude  required,         -       31°  18'  25" 

2.     The  apparent  altitude  of  the  sun's  center,  ivas  observed  to  be 
22°  12'  12",  what  was  its  true  altitude? 

Apparent  altitude,  22°  12'  12" 

From  the  table,         (Sub.)  2'  22" 


True  altitude,         -         -         22°     9'  50" 

3.     The  altitude  of  a  star  was  observed  to  be  8°  32',  what  was  its 
true  altitude  ? 

From,  -       8°  32'  00" 

Subtract  6'  9"  from  the  table,  6'     9" 


True  altitude,  at  that  time,         8°  25'  5l" 

Thus  we  might  add  examples  without  end. 

Let  it  be  borne  in  mind,  that  the  latitude  of  any  place  on  the 
earth,  is  the  inclination  of  its  zenith  to  the  plane  of  the  equator; 
which  inclination  is  equal  to  the  altitude  of  the  pole  above  the 
horizon. 

What  is  the  inclination  of  the  zenith  and  the  celestial  equator  equal  to? 


46  ELEMENTARY  ASTRONOMY. 

We  demonstrate  this  as  follows.     Let  E  represent  the  earth. 

Now  as  an  obser- 
ver always  conceives 
himself  to  be  on  the 
topmost  part  of  the 
earth,  the  vertical 
point,  Z,  truly  and 
naturally  represents 
his  zenith.  Through 
E,  draw  HE  0,  at  right  angles  to  EZ  ;  then  HE  0  will  rep- 
resent the  horizon  (for  the  horizon  is  always  at  right  angles  to 
the  zenith). 

Let  EQ  represent  the  plane  of  the  equator,  and  at  right 
angles  to  it,  from  the  center  of  the  earth,  must  be  the  earth's 
axis;  therefore,  EP,  at  right  angles  to  E Q,  is  the  direction  of 
the  pole. 

Now  the  arcs,       -      -      ZP+P  0=90°, 
Also,       -       -       -  :    •     ZP  +  ZQ=90°, 


By  subtraction,      -     -      PO  —  ZQ=0; 

Or,  by  transposition,  the  arc  PO=ZQ;  that  is,  the  alti- 
tude of  the  pole  is  equal  to  the  latitude  of  the  place ;  which 
was  to  be  demonstrated. 

In  the  same  manner,  we  may  demonstrate  that  the  arc  HQ 
is  equal  to  the  arc  ZP  ;  that  is,  the  polar  distance  of  the  zenith  is 
equal  to  the  meridian  altitude  of  the  celestial  equator.  Now,  we 
perceive,  that  by  knowing  the  latitude,  we  know  the  several 
divisions  of  the  celestial  meridian,  from  the  northern  to  the 
southern  horizon,  namely,  OP,  PZ,  ZQ,  and  QH. 

By  observing  the  extreme  altitudes  of  the  circumpolar  stars,  and 
correcting  such  altitudes  for  refraction,  the  half  sum  of  the  true  ex- 
treme altitudes  of  any  one  star,  will  be  the  latitude  of  the  place  of 
observation. 

What  place  is  the  earth's  axis  perpendicular  to?  What  is  the  altitude 
of  the  pole  equal  to  ?  What  is  the  polar  distance  of  the  zenith  equal  to  ? 


ATMOSPHERICAL  REFRACTION.  47 

We  give  an  example. 

The  greatest  observed  altitude  of  the  polar  star,     41°  37' 
Refraction,         -  -  1'  5" 


True  altitude,          -         -  41°  35'  55" 

The  least  observed  altitude  of  the  same  star,        38°  39'  15" 
Refraction, 1'  12" 


Least  true  altitude         ....      33°  38'     3" 

Greatest  true  altitude,         -          -  -     41°  35'  55" 


Sum, 80°  13'  58" 


Half  sum  latitude  -         -  -     40°     6'  59" 

We  might  take  any  other  circumpolar  star,  as  well  as  the 
pole  star  —  but  the  pole  star  is  the  least  liable  to  error,  because 
of  the  smaller  circle  it  describes. 

We  are  now  prepared  to  observe  and  record  the  declination 
of  the  stars,  or  any  heavenly  body. 

The  declination  of  a  star,  or  any  celestial  object,  is  its  meridian 
distance  from  the  celestial  equator. 

To  determine  the  declination  of  a  star,  we  must  observe  its 
meridian  altitude  (by  some  instrument,  say  the  mural  circle,) 
and  correct  the  altitude  for  refraction,  the  difference  will  be 
the  star's  true  altitude. 

If  the  true  meridian  altitude  of  the  star  is  less  than  the  meridian 
altitude  of  the  celestial  equator,  then  the  declination  of  the  star  is 
south.  If  the  meridian  altitude  of  the  star  is  greater  than  the  meri- 
dian altitude  of  the  equator,  then  the  declination  of  the  star  is 
north. 

These  truths  will  be  apparent  by  merely  inspecting  the  last 
figure. 

How  is  the  latitude  of  a  place  originally  determined  ?  What  is  under- 
stood by  the  declination  of  a  star  ?  When  the  declination  of  a  star  is  0, 
how  far  is  it  from  the  pole  ? 


48  ELEMENTARY  ASTRONOMY. 

EXAMPLES . 

1.  Suppose  an  observer  in  the  latitude  of  40°  12'  18"  north, 
observes  the  meridian  altitude  of  a  star,  from  the  southern  horizon, 
to  £e31°  36'  37";  whatis  the  declination  of  that  star  ? 

From  -     90°       0'     00" 

Take  the  latitude,         ...  40°     J2'     18" 


Diff.  is  the  meridian  alt.  of  the  equator,  49°     47'     42" 

Alt.  of  star,     31°     36'     37" 
Refraction,  1'     32" 

True  altitude,      31°     35'       5"     -      -     31°     35'       5" 


Declination  of  the  star,  south,     -         -   18°     12'     37" 

2.  The  same  observer  finds  the  meridian  altitude  of  another 
star,  from  the  southern  horizon,  to  be  79°  31'  42"  y  what  is  the  de- 
clination of  that  star? 

Observed  altitude,         -         -         -        79°     31'    42" 
Refraction,  ....  \\ 


True  altitude,         -         -         -          -         79      31      31 
Altitude  of  equator,     -         -         •         -    49      47      42 


Star's  declination,  north,          -         -         29°     43'     49" 

3.  The  same  observer,  and  from  the  same  place,  finds  the  meri- 
dian altitude  of  a  star,  from  the  northern  horizon,  to  be  51°  29' 
53"  /  what  is  the  declination  of  that  star  ? 


Observed  altitude, 

51° 

9.9' 

53" 

Refraction, 

46 

True  altitude  of  star, 

51 

29 

7 

Altitude  of  pole  (or  latitude), 

40 

12 

18 

Star  from  the  pole  (or  polar  dist.), 

11 

16 

49 

Polar  dist.,  from  90°,  gives  decl.  north, 

78° 

43' 

11" 

How  do  you  find  the  meridian  altitude  of  the  equator  ?     When  a  star 
comes  to  the  zenith,  how  can  we  find  its  declination  ? 


ATMOSPHERICAL  REFRACTION.  49 

In  this  way  the  declination  of  every  star  in  the  visible 
heavens  can  be  determined. 

In  Chapter  IV,  we  explained  how  to  obtain  the  difference 
of  the  right  ascension  of  the  stars,  and  this,  with  the  declination, 
mil  enable  us  to  mark  down  the  position  of  the  stars,  on  a  globe, 
and  thus  give  a  true  representation  of  the  appearance  of  the  heavens. 

Quite  a  region  of  stars  exists  around  the  south  pole,  which 
are  never  seen  from  these  northern  latitudes ;  and  to  observe 
them,  and  define  their  positions,  Dr.  Halley,  Sir  John  Her- 
schel,  and  several  other  English  and  French  astronomers, 
have,  at  different  periods,  visited  the  southern  hemisphere. 
Thus,  by  the  accumulated  labors  of  many  astronomers,  we  at 
length  have  correct  catalogues  of  all  the  stars  in  both  hemis- 
pheres, even  down  to  many  that  are  never  seen  by  the  naked 
eye. 

There  are  several  constellations  in  the  southern  regions, 
worthy  of  notice — the  Southern  Cross  and  the  Magellan  Clouds. 
The  Southern  Cross  very  much  resembles  a  cross ;  so  much  so, 
that  any  person  would  give  the  constellation  that  appellation. 
Its  principal  star  is,  in  the  right  ascension,  12  h.  20m.,  and 
south  declination  33°. 

The  Magellan  Clouds  were  at  first  supposed  to  be  clouds, 
by  the  navigator  Magellan,  who  first  observed  them.  They 
are  four  in  number ;  two  are  white,  like  the  Milky  Way,  and 
have  just  the  appearance  of  little  white  clouds.  They  are 
nebulce.  The  other  two  are  black — extremely  so  —  and  are 
supposed  to  be  places  entirely  devoid  of  all  stars ;  yet  they  are 
in  a  very  bright  part  of  the  Milky  Way — right  ascension 
10  h.  40m.,  decimation  62°  south. 

Can  \ve  see  all  the  stars  in  the  heavens  from  the  northern  latitudes  ? 
What  is  said  of  the  stars  in  the  southern  hemisphere  ?    What  are  the  Ma- 
gellan Clouds  ?    Have  they  all  a  similar  appearance  ? 
5 


50  ELEMENTARY  ASTRONOMY. 

CHAPTER  VI. 
SCIENTIFIC    METHODS    OF   FINDING    PARTICULAR    STARS. 

AMONG  our  tables  will  be  found  a  catalogue  of  one  hundred 
of  the  principal  stars,  inserted  for  the  purpose  of  teaching  the 
learner  the  scientific  method  of  defining  the  stars. 

To  have  a  clear  understanding  of  the  method  we  are  about 
to  explain,  we  must  again  consider  that  right  ascension  is 
reckoned  from  the  equinox,  eastward  along  the  equator,  from 
Oh.  to  24  hours.  When  the  sun  comes  to  the  equator,  in 
March,  its  right  ascension  is  0  ;  and  from  that  time  its  right 
ascension  increases  about  four  minutes  in  a  day,  through  the 
year,  to  24  hours  ;  and  then  it  is  again  at  the  eqninox,  and  the 
24  hours  are  dropped. 

But  whatever  be  the  right  ascension  of  the  sun,  it  is  appa- 
rent noon  when  it  comes  to  the  meridian  ;  and  the  more  east- 
ward a  body  is,  the  later  it  is  in  coming  to  the  meridian. 
Thus  :  If  a  star  comes  to  the  meridian  at  two  o'clock  in  the  after- 
noon (apparent  time),  *  it  is  because  its  right  ascension  is  TWO 
HOURS  GREATER  than  the  right  ascension  of  the  sun. 

Therefore,  if  from  the  right  ascension  of  a  star  we  subtract 
the  right  ascension  of  the  sun,  the  remainder  will  be  the  appa- 
rent time  for  that  star  to  come  to  the  meridian. 

If  we  put  (R^)  to  represent  the  star's  right  ascension,  and 
(R^)  to  represent  that  of  the  sun,  and  T  to  represent  the  ap- 
parent time  that  the  star  passes  the  meridian,  then  we  shall 
have  the  following  equation  : 


By  transposition         JR^=R 

•"We  will  explain  the  difference  between  apparent  time,  and  common 
clock  time,  in  a  future  chapter.  The  difference  is  never  17  minutes,  com- 
monly much  less, 

How  do  you  find  the  right  ascension  of  a  star,  or  any  heavenly  body  ? 


METHOD  OF  FINDING  PARTICULAR  STARS. 


51 


That  is,  to  find  the  right  ascension  of  a  star,  (or  any  heavenly 
body),  Add  the  right  ascension  of  the  sun  to  the  apparent  time  the 
body  is  observed  to  pass  the  meridian. 

The  right  ascension  of  the  sun  is  given,  in  the  Nautical 
Almanac  (and  in  many  other  almanacs),  for  every  day  in  each 
year,  when  the  sun  is  on  the  meridian  of  Greenwich ;  but 
many  of  the  readers  of  this  work  may  not  have  such  an  alma- 
nac at  hand,  and  for  their  benefit,  we  give  the  right  ascension 
for  every  fifth  day  of  the  year  1846,  in  the  following  table,  which 
will  show  the  right  ascension  for  the  same  day  in  any  other  year 
within  three  minutes  of  time  during  the  present  century,  and 
this  will  be  sufficiently  accurate  to  illustrate  the  principle. 

SUN'S  RIGHT  ASCENSION  FOR  1846. 


Day 
of 
Mo 

January. 

February. 

March. 

April. 

May. 

JOB*. 

h.  m.  s. 

h.  m.  s. 

h.  m.  s. 

1 
5 
10 
15 
20 
25 
30 

18  46  52 
19  4  30 
19  26  21 
19  47  57 
20  9  17 
20  30  19 
20  51  0 

20  59  11 
21  15  22 
21  35  18 
21  54  54 
22  14  12 
22  33  14 

22  48  17 
23  3  12 
23  21  40 
23  40  0 
23  58  14 
0  16  25 
0  34  36 

0  41  52 
0  56  26 
1  14  43 
1  33  6 
1  51  38 
2  10  22 
2  29  17 

2  23  6 
2  48  25 
3  7  47 
3  27  24 
3  47  15 
4  7  20 
4  27  18 

4  35  48 
4  52  12 
5  12  50 
5  33  34 
5  54  22 
6  15  10 
6  35  55 

Day. 
or 
Mo. 

July. 

August. 

September. 

October. 

November. 

December. 

1 
5 

10 
15 
20 
25 
30 

6  40  4 
6  56  34 
7  17  5 

7  37  25 
7  57  33 

8  17  28 
8  37  7 

8  44  55 
9  0  23 
9  19  29 
9  38  21 
9  56  60 
10  15  27 
10  33  44 

10  41   0 

10  55  29 
11  13  30 
11  3'1  28 
11  49  25 
12  7  24 
12  25  27 

12  29  4 
12  43  36 
13  1  54 
13  20  24 
13  39  8 
13  58  9 
14  17  27 

14  25  16 
14  41  2 
15  1  5 
15  21  28 
15  42  14 
16  3  19 
16  24  43 

16  29  1 
16  46  23 
17  8  17 
17  30  22 
17  52  33 
18  14  46 
18  36  57 

To  obtain  sufficient  data  to  apply  the  preceding  rule,  the 
observer  should  adjust  his  watch  to  apparent  time,  that  is, 
apply  the  equation  of  time,  or  in  other  words,  see  that  his  watch 
shows  12  o'clock  when  the  sun  is  on  the  meridian,  and  he 
must  know  the  direction  of  the  meridian  from  which  he  takes 
the  observations.  In  short,  by  the  range  of  definite  objects,  he 

When  is  it  apparent  noon  ? 


62  ELEMENTARY    ASTRONOMY 

must  be  able  to   decide,  within  two  or  three  minutes,  when  a 
celestial  body  is  on  the  meridian. 

Thus  being  all  prepared,  we  give  a  few 

EXAMPLES  . 

1.  Being  in  latitude  about  40°  north,  and  on  the  %Qth  of  May,  at 
9A.  27wi.  in  the  evening,  apparent  lime,  I  observed  a  lone  bright  star, 
of  about  the  %d  magnitude,  on  the  meridian.  I  had  no  instrument 
to  measure  its  altitude,  but  I  simply  judged  the  altitude  to  be  about 
42°  from  the  southern  horizon.  What  star  was  this? 

We  determine  it  thus: 

On  the  20th  of  May,  at  9  in  the  evening,  the  right  ascension 
of  the  sun  cannot  be  far  from,  -  -  3h  49m 

To  this  add  the  apparent  time  of  passing  the  merid.     9h  27m 


The  sum  is  the  right  ascension  of  the  star.         -        13h   16m 
By  inspecting  the  catalogue  of  stars,  we  find  the  right  as- 
cension of  Spica  is   registered  at    13h  17m  8s.,  therefore  it  is 
more  than  probable  that  the  star  observed  was  Spica. 

To  make  it  sure,  we  find  that  the  declination  of  Spica  in  the 
catalogue,  is  10°  21'  35"  south;  but  in  latitude  40°  north,  the 
meridian  altitude  of  the  celestial  equator  must  be  50°;  and  any 
stars  south  of  that  must  have  a  less  altitude.  Therefore,  the 
meridian  altitude  of  Spica  must  be  50°,  less  10°  21',  or  39° 
39';  but  the  star  I  observed,  I  simply  judged  to  have  had  an 
altitude  of  42°.  It  is  very  possible  that  I  should  err,  in  alti- 
tude, two  or  three  degrees  ;*  but,  it  is  not  possible  that  the  star  I 

*Ten  or  twenty  degrees,  near  the  horizon,  is  apparently  a  much  larger 
space  than  the  same  number  of  degrees  near  the  zenith.  Two  stars,  when 
near  the  horizon,  appear  to  be  at  a  greater  distance  asunder  than  when 
their  altitudes  are  greater.  The  variation  is  a  mere  optical  illusion  ;  fur, 
by  applying  instruments  to  measure  the  angle  in  the  different  situations, 
we  find  it  the  same.  Unless  this  fact  is  taken  into  consideration,  an  ob- 
server -will  always  conceive  the  altitude  of  any  object  to  be  greater  than  i< 
really  is,  especially  if  the  altitude  is  less  than  45  degrees. 

If  a  star  was  observed  to  pass  the  meridian  at  lOh  12m  in  the  evening 
when  the  sun's  right  ascension  was  2h  5m.,  what  must  have  been  the 
right  ascension  of  that  star? 


METHOD  OF  FINDING  PARTICULAR  STARS.  53 

observed  should  be  any  other  star  than  Spica;  for  there  is  no 
other  bright  star  near  it.     This  is  one  of  the  lunar  stars. 

Being*  now  certain  that  this  star  is  Spica,  I  can  observe  it  in 
relation  to  its  appearance  —  the  small  stars  that  are  near  it,  and 
the  clusters  of  stars  that  are  about  it — or  the  fact,  that  no  re- 
markable constellation  is  near  it.  In  short,  I  can  so  make  its 
acquaintance  as  to  know  it  ever  after ;  but  I  am  unable  to 
convey  such  acquaintance  to  others  by  language ;  true  know- 
ledge, in  this  particular,  demands  personal  observation. 

2.  On  the  3d  of  July,  at  9k  30m.  apparent  time,  in  the  evening, 
in  latitude  39°  north,  and  longitude  about  75°  west,  a  star  of  the 
first  magnitude  was  observed  to  pass  the  meridian.  The  star  was  of 
a  deep  red  color,  and,  as  near  as  my  judgment  could  decide,  its  alti- 
tude was  between  25°  and  30°.  Two  small  stars  were  near  it,  and  a 
remarkable  cluster  of  smaller  stars  were  west  and  northwest  of  it, 
at  the  distances  of  5°,  6°,  or  7°.  What  star  was  this? 

Sun's  right  ascension  at  the  time,         -         -      6h  50m 
Apparent  time  the  star  passed  meridian,        -      9h  30m 


Right  ascension  of  the  star,         -         -         -     16h  20m 

By  inspecting  the  catalogue  of  stars,  I  find  Antares  to  have  a 
right  ascension  of  16h.  20m.  2s.  and  a  decimation  of  26°  4', 
south. 

In  the  latitude  mentioned,  the  meridian  altitude  of  the  celes- 
tial equator  must  be  -  51°  0' 

Objects  south  of  that  plane  must  be  less,  hence  (sub.)  26°  54' 

Meridian  altitude  of  Antares,  in  lat.   39°  north,         24°  56' 

As  the  observation  corresponds  to  the  right  ascension  of  An* 

tares  (a»  nearly  as  possible,  considering  errors  in  observations, 

and  probably  in  the  watch),  and  as  the  altitudes  do  not  differ 

many  degrees  (within  the  limits  of  guess  work),  it  is  certain 

Can  anyone  recognize  particular  stars  in  the  heavens  without  personal 
observation  ?  In  the  2d  example,  how  do  we  know  that  the  star  observed 
was  Autares  ?  What  is  the  right  ascension  of  Antares  ? 


64  ELEMENTARY  ASTRONOMY. 

that  the  star  observed  was  ANTARES.  By  its  peculiar  red  color, 
and  the  remarkable  clusters  of  stars  surrounding  it,  I  shall  be 
able  to  recognize  this  star  again,  without  the  trouble  of  direct 
observation. 

3.  On  the  night  of  the  ZQth  of  June,  in  latitude  40°  north  and 
longitude  75°  west,  at  \h  47m.  past  midnight,  apparent  time,  a  star 
of  the  first  magnitude  was  observed  to  pass  the  meridian  :  two  other 
stars  of  about  the  third  magnitude  were  within  3°  of  it;  the  three  stars 
forming  nearly  a  right  line  north  and  south ;  the  altitude  of  the 
principal  stars  from  the  south  was  about  60°.  What  star  was  it  ? 

In  these  examples,  the  time  must  be  reckoned  from  noon  to 
noon  again,  24  hours,  and  if  the  sum  of  any  addition  exceeds 
24  hours,  the  excess  only  must  be  taken. 

In  this  example,  Ih  47m  after  midnight  must  be  written  13h 
47m. 

The  longitude  of  75°  west,  also  adds  5  hours  to  the  Green- 
wich time,  hence  the  time  that  this  star  passed  the  meridian, 
was  June  20th,  the  18th  hour  of  that  day,  within  6  hours  of  the 
21st  of  June.  To  this  time  we  compute  the  sun's  right  ascen- 
sion. 

Sun's  right  ascension  at  the  time  the  star  was  on  the  meri- 
dian could  not  be  far  from,         ...          -       5h  58m 
To  this  add,       -  13     47 

Sum,  is  the  right  ascension  of  the  star,          -         19h  45m. 

By  inspecting  the  catalogue  of  stars,  we  find  the  right  as- 
cension of  Altair  19  h.  43  m.  15s.,  and  its  declination  8°  27'  N". 
In  latitude  40°  N.,  the  declination  of  8°  27'  N.  will  give  a  me- 
ridian altitude  of  55°  27';  and,  in  short,  I  know  the  star  ob- 
served must  be  Altair,  and  the  two  other  stars,  near  it,  I  recog- 
nize in  the  catalogue. 

What  is  the  color  of  Antares  ?  Is  there  a  cluster  of  stars  near  Antares,  and 
in  what  direction  ?  Suppose  the  time  is  after  midnight,  how  do  you  reckon 
it  ?  If  the  sum  found  by  adding  the  right  ascension  of  the  sun  to  the  time  a 
body  passed  the  meridian,  should  exceed  24  hours,  what  would  you  do  ? 


METHOD  OF  FINDING  PARTICULAR  STARS.  55 

By  taking  these  observations,  any  person  may  become  ac- 
quainted with  all  the  principal  stars,  and  the  general  aspect  of 
the  heavens ;  but  no  efforts,  confined  merely  to  the  study  of 
books,  will  accomplish  this  object. 

The  rule  here  used  is  not  solely  confined  to  the  stars,  it  is 
applicable  to  any  heavenly  body,  moon,  comet,  or  planets,  and  if 
the  foregoing  examples  are  understood,  the  reader  will  have  a 
good  general  idea  how  the  right  ascension  of  the  moon,  and 
planets,  are  from  time  to  time,  determined  by  observation. 

The  time  of  passing  the  meridian  is  relatively  but  another 
term  for  right  ascension,  and  if  observations  are  made  on  any 
bright  star,  and  no  corresponding  star  is  to  be  found  in  the 
catalogue,  such  a  star  would  probably  be  found  to  be  a  planet, 
and  if  a  planet,  its  right  asension  will  change. 

WE    MAT    NOW    REVERSE    THE    PROBLEM. 

Suppose  that  we  wish  to  find  any  particular  star,  for  example, 
Aldebaran. 

It  is  a  clear  star  light  night,  January  19th,  the  sun's  right 
ascension  by  the  Nautical  Almanac,  I  find  approximately  to 
be  about  20h.  5m.,  and  in  the  catalogue  of  stars  I  find  the 
right  ascension  of  Aldebaran  to  be  4h.  27m.  disregarding  the 
seconds. 

The  equation,  R^fc  —  fiQ=T  is  general,  and  shows  us  that 
we  must  subtract  the  right  ascension  of  the  sun  from  the  right 
ascension  of  the  star,  and  the  remainder  is  the  apparent  time 
that  the  star  comes  to  the  meridian.  To  render  the  subtrac- 
tion possible,  we  must  in  some  cases  increase  the  right  ascen- 
sion of  the  star  by  24  hours. 

h.    m. 

From  ^^--(-24  hours            -         -         -         28  27 
Subtract  20     5 


Aldebaran  on  the  meridian  (Jan.  19th),     -  8  22 

How  can  we  find  the  right  ascension  of  the  moon,  or  a  planet,  by  obser- 
vation ?  How  do  we  find  the  time  when  any  particular  star  will  pass  the 
meridian  ? 


66  ELEMENTARY  ASTRONOMY. 

This  shows,  that  if  the  stars  are  visible  on  the  19th  of  Jan- 
uary, of  any  year,  and  we  look  along  the  meridian  at  about  20 
minutes  after  8  in  the  evening,  we  shall  certainly  see  Aldebaran. 

Suppose  it  the  10th  of  March,  of  any  year,  and  a  learner 
wishes  to  be  sure  of  finding  the  star  Sirius. 

He  must  inspect  the  catalogue  of  stars,  and  he  will  find  its 
right  ascension  to  be  6h.  38m. ;  and  by  the  table  on  page  51, 
or  better,  by  a  Nautical  Almanac,  he  will  find  the  right  ascen- 
sion of  the  sun,  on  the  10th  of  March,  to  be  not  far  from  23h. 

22m.,  therefore 

h.    m. 
From  R%-  6h.  38m.+24h.        -     30  38 

Subtract  23  22 

Sirius  on  the  meridian,  March  10th,      716     apparent  time. 

Now,  if  on  that  day  of  the  year,  at  about  16  minutes  past  7, 
apparent  time  in  the  evening,  we  observe  the  heavens,  we  shall 
certainly  see  Sirius  in  a  southern  direction,  and  by  taking  into 
consideration  our  latitude  and  the  declination  of  the  star,  we 
can  form  a  very  correct  estimate  of  its  altitude,  and  we  could 
as  readily  find  the  star  as  we  could  find  the  moon. 

In  this  manner  we  may  find  when  any  particular  star  will  come 
to  the  meridian,  and  take  that  time  to  observe  it.  Speaking  loosely, 
the  same  star  comes  to  the  meridian  at  the  same  hour  and 
minute,  sidereal  time,  througout  the  year,  but  at  different  times, 
on  different  days,  by  the  solar  clock.  On  account  of  the  sun 
changing  its  right  ascension  from  day  to  day,  sidereal  time  is  in 
fact  right  ascension. 

Do  the  stars  come  to  the  meridian  at  the  same  time  throughout  the  year, 
by  the  sidereal  clock  ?  Why  then  do  they  vary  by  the  solar  or  common 
clock? 


FIGURE  AND  MAGNITUDE  OF  THE  EARTH.  57 

CHAPTER   VII. 
PLANETS  — FIGURE  AND  MAGNITUDE  OF  THE  EARTH. 

In  the  preceding  chapter,  we  have  been  careful  to  impress 
the  fact,  that  the  great  mass  of  the  stars  pass  the  meridian  at 
regular  intervals  of  time,  and  that  the  same  star  will  pass  the 
meridian  at  intervals  of  24  sidereal  hours,  which  corresponds  to 
23h.  56m.  4.09s.  of  mean  solar  time. 

If  sidereal  time  of  24h.  between  the  passage  of  the  same  star 
over  the  meridian  is  taken  for  the  standard  measure  of  time, 
then  the  mean  intervals  between  two  consecutive  passages  of 
the  sun  across  the  meridian  is  24h.  3m.  56.5t554s. 

We  say  mean  interval,  because  this  interval  is  not  always 
the  same,  and  not  being  the  same,  gives  rise  to  the  equation  of 
time.  The  cause  of  this  inequality,  and  consequently  the  cause 
of  the  equation  of  time,  will  be  examined  hereafter;  the  fact  was 
first  observed  by  noting  the  passage  of  the  sun  across  the  meri- 
dian, in  comparison  with  a  well  regulated  sidereal  clock. 

All  those  stars  that  pass  the  meridian  at  equal  intervals  ot 
time,  and  always  at  the  same  altitude,  if  observed  from  the 
same  station,  are  called  and  must  be  in  fact,  fixed  stars,  but  the 
sun  coming  to  the  meridian  at  unequal  intervals  of  time,  and  at 
different  altitudes  from  the  horizon,  shows  that  it  is  not  &  fixed 
body. 

When  we  compare  the  times  of  the  moon  passing  the  meri- 
dian, with  the  astronomical  clock,  we  are  very  forcibly  struck 
with  the  irregularity  of  the  interval. 

The  least  interval  between  two  successive  transits  of  the 
moon  (which  may  be  called  a  lunar  day),  is  observed  to  be 

What  has  the  author  been  careful  to  impress,  in  the  previous  chapter? 
What  astronomical  interval  is  always  the  same?  Does  the  sun  come  to 
the  meridian  at  equal  intervals  of  time  ?  To  what  does  this  give  rise  ? 


58  ELEMENTARY  ASTRONOMY. 

about  24h.   42m. ;  the  greatest,  25h.  2m, ;  and  the  mean,  or 
average,  24h.  54m.,  of  mean  solar  time. 

These  facis  show,  conclusively,  that  the  moon  is  not  a  fixed 
body,  like  a  fixed  star,  for  then  the  interval  would  be  24  hours 
of  sidereal  time. 

But  as  the  interval  is  always  more  than  24  hours,  it  shows 
that  the  general  motion  of  the  moon  is  eastward,  among  the 
stars,  with  a  daily  motion  varying  from  10-J  to  16  degrees, 
traveling,  or  appearing  to  travel,  through  the  whole  circle  of 
the  heavens  (360°)  in  a  little  more  than  27  days. 

Thus  these  observations,  however  imperfectly  and  rudely 
taken,  at  once  disclose  the  important  fact,  that  the  sun  and 
moon  are  in  constant  change  of  position,  in-  relation  to  the 
stars,  and  to  each  other;  and  we  may  add,  that  the  chief  ob-, 
ject  and  study  of  astronomy,  is,  to  discover  the  reality,  the 
causes,  the  nature,  and  extent  of  such  motions. 

Besides  the  sun  and  moon,  several  other  bodies  were  noticed 
as  coming  to  the  meridian  at  very  unequal  intervals  of  time, 
intervals  not  differing  so  much  from  24  sidereal  hours  as  the 
moon,  but,  unlike  the  sun  and  moon,  the  intervals  were  some- 
times less,  sometimes  greater,  and  sometimes  equal  to  24  side- 
real hours. 

These  facts  show  that  these  bodies  have  a  real,  or  apparent 
motion,  among  the  stars,  which  is  sometimes  westward,  some- 
times eastward,  and  sometimes  stationary  ;  but,  on  the  whole, 
the  eastward  motion  predominates ;  and,  like  the  sun  and 
moon,  they  finally  perform  revolutions  through  the  heavens 
from  west  to  east. 

On\y  four  such  bodies  (stars)  were  known  to  the  ancients, 
namely,  Venus,  Mars,  Jupiter,  and  Saturn. 

These  stars  are  a  portion  of  the  planets  belonging  to  our  solar 
system,  and,  by  subsequent  research,  it  was  found  that  the 
Earth  was  also  one  of  the  number.  As  we  come  down  to 
more  modern  times,  several  other  planets  have  been  discovered, 

What  direction  does  the  moon  move  in  respect  to  the  fixed  stars  ?  Ho\v 
many  degrees  does  it  move  in  a  day  ?  In  how  many  days  will  it  make  a 
revolution  ?  "What  other  wandering  bodies  were  observed  by  the  ancients  ? 


FIGURE  AND  MAGNITUDE  OF  THE  EARTH.  59 

namely  Mercury,  Uranus,  Vesta,  Juno,  Ceres,  Pallas,  and  very 
recently,  Neptune,  Iris,  Hebe,  Flora,  Astrea,  and  one  or  two 
others  of  no  moment  to  record  in  a  work  like  this. 

We  here  mention  the  names  of  these  planets  in  the  order  of 
their  discovery,  and  not  in  the  order  in  which  they  revolve  in 
the  system,  for  as  yet  we  have  no  definite  idea  of  a  planet  or  a 
planetary  system.  In  the  tables,  they  will  be  found  in  their 
proper  order  in  reference  to  the  center  of  the  system. 

It  is  unreasonable  and  unnatural  to  suppose  that  the  appa- 
rent motions  of  these  wandering  stars  are  their  real  motions,  as 
viewed  from  a  stationary  point;  such  irregularities  in  apparent 
motions  can  only  be  accounted  for,  on  the  supposition  that  the 
observer,  on  the  earth,  that  is,  the  earth  itself,  is  in  motion  as 
well  as  the  planets. 

The  ancients,  taking  the  first  impressions  of  their  senses, 
supposed  the  earth  to  be  a  plane,  and  the  principal  object  in  the 
universe,  and  under  this  idea  the  planetary  motions  were  inex- 
plicable; but  we  shall  not  pretend  to  explain  the  slow  process 
of  knowledge  which  gradually  melted  away  this  erroneous  im- 
pression, we  shall  simply  bring  forth  science,  as  it  is  now 
known  to  exist,  and  therefore  we  must  now  consider  the 

t    FIGURE    AND    MAGNITUDE    OF    THE    EARTH. 

The  greater  portion  of  the  surface  of  the  earth  is  water,  and 
the  surface  of  water  is  every  where  convex,  as  any  observer  may 
convince  himself  who  takes  the  opportunity  to  do  so.  In 
coming  in  from  sea,  the  high  land,  back  in  the  country,  is  seen 
before  the  shore,  which  is  nearer  to  the  observer ;  the  tops  of 
trees,  and  the  tops  of  towers,  are  seen  before  their  bases.  Tf 


mssm 


Is  it  probable  that  very  irrearnlar  motions,  such  as  we  observe  in  the 
planets,  are  real  motions  ?  Did  the  ancients  suppose  the  earth  to  be  a 
plane  ?  How  dp  we  know  that  it  is  not  a  plane  ? 


60  ELEMENTARY  ASTRONOMY. 

the  observer  is  on  shore,  viewing  an  approaching  vessel,  he 
sees  the  topmast  first ;  and  from  the  top,  downward,  the  vessel 
gradually  comes  in  view.  These  facts  are  sufficiently  illustra- 
ted by  the  adjoining  figure. 

One  of  the*  most  striking  observations  of  this  kind,  is  made 
in  the  Mediterranean  sea.  On  the  island  of  Minorca,  near  its 
center,  stands  Mount  Toro,  and  on  the  very  vertex  of  the  moun- 
tain stands  a  Monastery,  three  stories  high. 

On  approaching  the  island  from  any  direction,  in  moderate 
and  clear  weather,  the  first  object  that  comes  to  view  is  the  top 
of  the  Monastery,  and  approaching  nearer,  the  upper  story  with 
its  windows,  becomes  distinctly  visible  —  continuing  to  ap- 
proach, the  whole  building  gradually  becomes  visible,  standing 
apparently  alone  on  the  surface  of  the  sea.  Then  the  mountain 
itself  appears  to  rise,  and  finally,  the  island  and  shores  around. 
Similar  observations  are  made  every  day,  on  every  sea,  and  on 
every  portion  of  the  earth,  which  shows  to  a  demonstration 
that  the  earth  is  convex  on  every  part,  hence  it  must  be  a  globe 
or  sphere,  or  nearly  so. 

In  addition  to  this,  the  earth  has  been  circumnavigated  many 
times,  and  navigators  make  their  computations  on  the  supposi- 
tion that  the  earth  is  a  sphere,  and  this  supposition,  at  all 
times  corresponding  to  fact,  settles  the  question. 

To  this,  we  will  simply  call  to  mind  the  fact,  that  the  shadow 
of  the  earth,  on  the  moon,  in  eclipses  of  the  moon,  is  always 
circular,  which  could  not  always  be  the  case  if  the  earth  had 
any  other  shape  than  that  of  a  sphere. 

On  the  supposition  that  the  earth  is  a  sphere,  there  are  sev- 
eral methods  of  measuring  it,  without  the  labor  of  applying  the 
measure  to  every  part  of  it.  The  first,  and  most  natural 
method  (which  we  have  already  mentioned),  is  that  of  measu- 
ring any  definite  portion  of  the  meridian,  and  from  thence 
computing  the  value  of  the  whole  circumference. 

What  is  said  of  the  Monastery  on  the  island  of  Minorca  ?  What  is  said 
of  the  shadow  of  the  earth  ?  If  the  earth  is  spherical,  how  can  we  measure 
it,  without  measuring  entirely  round  ? 


FIGURE  AND  MAGNITUDE  OF  THE  EARTH.  61 

Thus,  if  we  can  know  the  number  of  degrees,  and  parts  of  a 
degree,  in  the  arc  AB,  and  then  measure  the  distance  in  miles, 
we  in  fact  virtually  know  the  whole  circumference;  for  what- 
ever part  the  arc  AB  is  of  360  degrees,  the  same  part,  the 
number  of  miles  in  AB,  is  of  the  miles  in  the  whole  circum- 
ference. 

That  is,  as  the  arc  AB  is  to  the  whole  circumference  360°,  so  is 
the  number  of  miles  in  AB  to  the  number  of  miles  in  tke  circum- 
ference. 

To  find  the  arc  AB,  the  latitude  of  the  two  points,  A  and  By 
must  be  very  accurately  taken,  and  their  difference  will  give 
the  arc  in  degrees,  minutes,  and  seconds.  Now  AB  must  be 
measured  simply  in  distance,  as  miles,  yards,  or  feet;  but  this  is 
a  laborious  operation,  requiring  great  care  and  perseverance. 
To  measure,  directly,  any  considerable  portion  of  a  meridian,  is 
indeed  impossible,  for  local  obstructions  would  soon  compel  a 
deviation  from  any  definite  line  ;  but  still  the  measure  can  be 
continued,  by  keeping  an  account  of  the  deviations,  and  redu- 
cing the  measure  to  a  meridian  line. 

When  we  know  the  hight  of 
a  mountain,  as  represented  in 
this  figure,  and  at  the  same 
time  know  the  distance  of  its 
visibility  over  the  surface  of 
the  earth  ;  that  is,  know  the 
line  MA;  then  we  can  com- 
pute the  line  M'G,  by  a  simple 
theorem  in  geometry  ;  thus, 


Now  as  the  right  hand  mem- 


How  do  we  find  the  arc  AB  ?  How  do  we  find  the  length  of  the  arc  in 
miles  or  feet  ?  What  rule  have  we  to  find  the  diameter  of  the  earth,  when 
we  know  the  hight  of  a  mountain,  and  the  distance  of  the  visible  horizon 
therefrom  ? 


62  ELEMENTARY  ASTRONOMY. 

ber  of  this  equation  is  known,  CM\&  known  ;  and  as  part  of  it 
(MB)  is  already  known,  the  other  part,  EG,  the  diameter  of 
the  earth,  thus  becomes  known. 

This  method  would  be  a  very  practical  one,  if  it  were  not  for 
the  uncertainty  and  variable  nature  of  refraction  near  the 
horizon  ;*  and  for  this  reason,  this  method  is  never  relied 
upon,  although  it  often  well  agrees  with  other  methods.  As 
an  example  under  this  method,  we  give  the  following : 

A  mountain,  two  miles  in  perpendicular  hight,  was  seen 
from  sea  at  a  distance  of  126  miles.  •  If  these  data  are  correct, 
what  then  is  the  diameter  of  the  earth  ? 

Solution:    J/C=^— ^=63 XI 26=7938.     .#£=7936. 

This  same  ^geometrical  theorem  serves  to  compute  the  dip  of 
the  horizon.  The  true  horizon  is  at  right  angles  from  the  zenith  ; 
but  the  navigator,  in  consequence  of  the  elevation  of  his  vessel, 
can  never  use  the  true  horizon ;  he  must  use  the  sea  offing, 
making  allowance  for  its  dip.  If  the  navigator's  eye  were  on  a 
level  with  the  sea,  and  the  sea  perfectly  stable,  the  true  and 
apparent  horizon  would  be  the  same.  But  the  observer's  eye 
must  always  be  above  the  sea  ;  and  trfe  higher  it  is,  the  greater 
the  dip  ;  and  the  amount  of  dip  will  depend  on  the  hight  of  the 
eye,  and  the  diameter  of  the  earth.  The  difference  between 
the  angle  AMC,  and  a  right  angle  (which  is  equal  to  the 
angle  AEM),  is  the  measure  of  the  dip  corresponding  to  the 
hight  BM. 

For  the  benefit  of  navigators,  a  table  has  been  formed,  show- 
ing the  dip  for  all  common  elevations. 

No  one  should  object  to  considering  the  earth  a  sphere, 
because  its  surface  is  diversified  with  mountains  and  valleys, 
for  the  highest  mountain  on  the  earth  is  not  so  large,  compared 

^Sometimes  a  distant  object  over  sea  appears  distinctly  visible,  and  at 
other  times  appears  depressed  below  the  horizon. 

What  objection  is  there  to  the  last  mentioned  method  of  measuring  the 
earth  ?  What  is  the  dip  of  the  horizon  ?  If  the  observer's  eye  were  down 
on  the  level  of  the  sea,  would  there  be  any  dip  ? 


FIGURE  AND  MAGNITUDE  OF  THE  EARTH.  63 

to  the  earth  itself,  as  a  fine  grain  of  sand  is  compared  to  a 
globe  of  18  inches  in  diameter.  No  one  objects  to  calling  an 
orange  round, because  of  the  roughness  of  its  external  surface. 

After  correct  views  were  entertained,  as  to  the  magnitude 
of  the  earth,  and  its  revolution  on  an  axis,  philosophers  con- 
cluded that  its  equatorial  diameter  might  be  greater  than  its 
polar  diameter ;  and  investigations  have  been  made  to  decide 
that  fact. 

If  the  earth  were  exactly  spherical,  it  is  plain  that  the  cur- 
vature over  its  surface  would  be  the  same  in  every  latitude  ; 
but  if  not  of  that  figure,  a  degree  would  be  longer  on  one  part 
of  the  earth  than  on  another.  "But,"  says  Herschel,  "when 
we  come  to  compare  the  measures  of  meridians!  arcs  made  in 
various  parts  of  the  globe,  the  results  obtained,  although  they 
agree  sufficiently  to  show  that  the  supposition  of  a  spherical 
figure  is  not  very  remote  from  the  truth,  yet  exhibit  discord- 
ances far  greater  than  what  we  have  shown  to  be  attributable 
to  errors  of  observation  ;  and  which  render  it  evident  that  the 
hypothesis,  in  strictness  of  its  wording,  is  untenable.  Without 
troubling  the  reader  with  the  details  of  actual  measurement, 
which  have  been  made  from  time  to  time  with  all  care  and 
precision,  it  is  sufficient  to  state  that  the  measured  length  of  a 
degree  increases  with  the  latitude,  being  greatest  near  the  poles 
and  least  near  the  equator,  giving  the  following  magnitude  of 
the  earth : 

Greatest,  or  equatorial  diameter,       7924.65  miles. 
Least,  or   polar  diameter,  7899.17 

Diff.  or  polar  compression,  26.48 

The  proportion  of  the  diameters  is  very  nearly  that  of-298  to 
299,  and  their  diff.  ^^  of  the  greater,  or  a  very  little  over 
3-3-75.  The  shape  of  the  earth,  thus  ascertained  by  actual  meas- 
urement, is  just  what  theory  would  give  to  a  body  of  water 
equal  to  our  globe,  and  revolving  on  an  axis  in  24  hours ;  and 

Is  the  earth  exactly  spherical,  aside  from  the  roughness  of  its  surfaced 
How  was  the  shape  of  the  earth  determined  ?  What  is  the  length  of  the 
equatorial  diameter  ?  What  of  the  polar  ? 


64  ELEMENTARY  ASTRONOMY. 

this  has  caused  many  philosophers  to  suppose  that  the  earth 
was  formerly  in  a  fluid  state. 

If  the  earth  were  a  sphere,  a  plumb  line  at  any  point  on  its 
surface  would  tend  directly  towards  the  center  of  gravity  of 
the  body  ,-but  the  earth  being  an  ellipsoid,  or  an  oblate  spheroid, 
and  the  plumb  lines,  being  perpendicular  to  the  surface  at  any 
point,  do  not  tend  to  the  center  of  gravity  of  the  figure,  but  to 
different  points,  as  represented  in  the  figure. 

The  plumb  line  at  H  tends  to  F, 
yet  the  mathematical  center,  and 
center  of  gravity  of  the  figure,  is 
at  E.  So  at  7,  the  plumb  line 
tends  to  the  point  G;  and  as  the 
length  of  a  degree  at  A,  is  to  the 
length  of  a  degree  at  H,  so  is  A  G 
to  HF.  If,  however,  a  passage 
were  made  through  the  earth,  and  a  body  let  drop  through  it, 
the  body  would  not  pass  from  /  to  G:  its  first  tendency  at  / 
would  be  toward  the  point  G;  but  after  it  passed  below  the 
surface  at  /,  its  tendency  would  be  more  and  more  toward  the 
point  E,  the  center  of  gravity ;  buc  it  would  not  pass  exactly 
through  that  point,  unless  dropped  from  the  point  A,  or  the 
point  C. 

If  the  earth  were  a  perfect  and  stationary  sphere,  the  force 
of  gravity,  on  its  surface,  would  be  everywhere  the  same ;  but, 
it  being  neither  stationary,  nor  a  perfect  sphere,  the  force  of 
gravity,  on  the  different  parts  of  its  surface,  must  be  different. 
The  points  on  its  surface,  nearest  its  center  of  gravity,  must 
have  more  attraction  than  other  points  more  remote  from  the 
center  of  gravity ;  and  if  those  points  which  are  more  remote 
from  the  center  of  gravity  have  also  a  rotary  motion,  there  will 
be  a  diminution  of  gravity  on  that  account. 

What  caused  philosophers  to  suppose  that  the  earth's  equatorial  diame- 
ter was  greater  than  its  polar  diameter  ?  Does  the  plumb  line  always  tend 
towards  the  mathematical  center  of  the  earth  ?  Does  it  always  tend  per 
pendicularly  to  the  surface  of  still  water  ? 


FIGURE  AND  MAGNITUDE  OF  THE  EARTH.  65 

Let  A  B  in  the  figure,  represent  the  equatorial  diameter  of 
the  earth,  and  CD  the  polar  diameter ;  and  it  is  obvious  that 
E  will  be  the  center  of  gravity,  of  the  whole  figure,  aird  that 
the  force  of  gravity  at  C  and  D  will  be  greater  than  at  any 
other  points  on  the  surface,  because  EC,  or  ED,  are  less  than 
any  other  lines  from  the  point  E  to  the  surface  .  The  force  of 
gravity  will  be  greatest  on  the  points  C  and  D.  also,  because 
they  are  stationary  :  all  other  points  are  in  a  circular  motion ; 
and  circular  motion  has  a  tendency  to  depart  from  the  center 
of  motion,  and,  of  course,  to  diminish  gravity.  The  diminution 
of  the  earth's  gravity  by  the  rotation  on  its  axis,  amounts  to 
its  2^-g-th  part*  at  the  equator.  By  this  fraction,  then,  is  the 
weight  of  the  sea  about  the  equator  lightened,  and  thereby 
rendered  susceptible  of  being  supported  at  a  higher  level  than 
at  the  poles,  where  no  such  counteracting  force  exists. 

It  is  this  centrifugal  force  itself  that  changed  the  shape  of 
the  earth,  and  made  the  equatorial  diameter  greater  than  the 
polar.  Here,  then,  we  have  the  same  cause,  exercising  at  once 
a  direct  and  an  indirect  influence.  Owing  to  the  elliptic  form 
of  the  earth,  and  independently  of  the  centrifugal  force,  its 
attraction  ought  to  increase  the  weight  of  a  body,  in  going 
from  the  equator  to  the  pole,  by  nearly  its  y£0-th  part;  which, 
together  with  the  ^-^th  part,  due  from  centrifugal  force,  make 
the  whole  quantity  yf^tli  part;  that  is,  194  pounds  pressure  at 
the  equator,  will  press  with  a  force  of  195  pounds  when  carried 
to  the  poles,  which  corresponds  with  the  result  of  observations 
deduced  from  the  vibrations  of  pendulums. 

The  form  of  the  earth  is  so  nearly  a  sphere,  that  it  is  con- 
sidered such,  in  geography,  navigation,  and  in  the  general 
problems  of  astronomy. 

*For  the  computation  which  brings  this  result,  see  the  university  edition 
of  Astronomy. 

Give  two  distinct  reasons  why  the  force  of  attraction  is  greater  at  the 
poles  than  at  the  equator?     In  what  proportion  do  bodies  increase  in 
weight  on   being   carried   from  the   equator  to  the  poles? 
6 


66  ELEMENTARY  ASTRONOMY. 

The  average  length  of  a  degree  is  69|-  English  miles ;  and, 
as  this  number  is  fractional,  and  inconvenient,  navigators  have 
tacitly  agreed  to  retain  the  ancient,  rough  estimate  of  sixty 
miles  to  a  degree  ;  calling  the  mile  a  geographical  mile.  There- 
fore, the  geographical  mile  is  longer  than  the  English  mile. 

As  all  meridians  come  together  at  the  pole,  it  follows  that  a 
degree,  between  the  meridians,  will  become  less  and  less  as 
we  approach  the  pole  ;  and  it  is  an  interesting  problem  to  trace 
the  law  of  decrease. 

This  law  will  become  apparent,  by  inspecting  the  figure  in 
the  margin. 

Let  EQ  represent  a  degree,  on 
the  equator,  and  JSQCa.  sector  on 
the  plane  of  the  equator,  and  of 
course  EC  is  at  right  angles  to  the 
axis  CP.  Let  DFI  be  any  plane 
parallel  to  EQC\  then  we  shall 
have  the  following  proportion  ; 
EC  :  DI.  :  :  EQ  :  DF. 
In  trigonometry,  EC  is  known  as  the  radius  of  the  sphere  ; 
DI  as  the  cosine  of  the  latitude  of  the  point  D  (the  numerical 
values  of  sines  and  cosines,  of  all  arcs,  are  given  in  trigonome- 
trical tables):  therefore  we  have  the  following  rule,  to  compute 
the  length  «f  a  degree  between  two  meridians,  on  any  parallel 
of  latitude' 

RULE. — As  radius  is  to  the  cosine  of  the  latitude,  so  is  the 
length  of  a  degree  on  the  equator,  to  the  length  of  a  parallel  degree 
in  that  latitude. 

We  gi^e  the  following  as  an  example,  although  pupils  will 
not,  and  cannot  fully  comprehend  it,  unless  they  are  acquainted 
with  trigonometry. 

What  is  the  average  length  of  a  degree  on  the  earth  ?  What  is  the 
differenre  between  an  English  and  a  geographical  mile  ?  By  what  rule  do 
two  mer.dians  approach  each  other  between  the  equator  and  the  poles  ? 


FIGURE  AND  MAGNITUDE  OF  THE  EARTH.  67 

Calling  a  degree,  on  the  equator,  60  miles,  what  is  the 
length  of  a  degree  of  longitude,  in  latitude  42°  ? 

SOLUTION    BY    LOGARITHMS. 

As  radius  (see  tables),  -         -         -     10.000000 

Is  to  cosine  42°  (see  tables),     -  -  9.871073 

So  is  60  miles  (log.),     -  1.778151 

To  44,-VA  miles,  Ans.  -        1.649224 

At  the  latitude  of  60°,  the  degree  of  longitude  is  30  miles ; 
the  diminution  is  very  slow  near  the  equator,  and  very  rapid 
near  the  poles. 

In  navigation,  the  DF's  are  the  known  quantities  obtained 
by  the  estimations  from  the  log  line,  etc. ;  and  the  navigator 
wishes  to  convert  them  into  longitude,  or,  what  is  the  same 
thing,  he  wishes  to  find  their  values  projected  on  the  equator, 
and  he  states  the  proportion  thus : 

DI    :     EC     :  :     DF    :     EQ ; 

That  is,  as  cosine  of  latitude,  is  to  radius,  so  is  departure,  to  differ- 
ence of  longitude. 

If  we  take  one  mile,  (either  the  English  or  the  Nautical 
mile),  for  the  distance  between  two  meridians  on  the  equator; 
the  distance  between  the  same  two  meridians  in  any  latitude 
will  be  expressed  by  the  cosine  of  that  latitude  in  any  table  of 
natural  cosines.* 

Thus,  Inspecting  a  table  of  natural  cosines  we  find  that  in 
lat.  25°  the  cosine  is  0.906.  That  is,  the  distance  of  one 
mile  on  the  equator,  corresponds  to  the  parallel  distance  of 
.906,  25  degrees  distant  from  the  equator.  Or  10  miles  on  the 
equator  corrresponds,  to  9.T$T  miles  in  lat.  25°.  In  Naviga- 
tion, the  distance  on  the  equator  is  called  difference  of  longi- 
tude, and  the  corresponding  distance  is  called  departure. 

We  might  have  taken  any  other  latitude  for  an  example  as 
well  as  25°.  Thus,  the  decimal  cosine  of  any  latitude  corresponds 
to  one  mile  on  the  equator. 

*Such  a  table  is  to  be  found,  between  pages  21  and  65,  of  our  tables, 
and  bound  in  each  of  the  tliree  volumes,  of  Robinson's  Mathematics,  viz. 
In  the  Geometry,  the  Surveying  and  Navigation,  and  in  the  Mathematical 
Operations. 


68  ELEMENTARY  ASTRONOMY. 

SECTION   II. 

DESCRIPTIVE     ASTRONOMY 

CHAPTER  I. 

FIRST    CONSIDERATIONS    AS    TO    THE    DISTANCES    OF    THE    HEAVENLY 
BODIES. LUNAR    PARALLAX    AND    DISTANCE    TO    THE    MOON. 

HITHERTO  we  have  considered 
only  appearances,  and  have  not 
made  the  least  inquiry  as  to  the 
nature,  magnitude,  or  distances  of 
the  celestial  objects. 

Abstractly,  there  is  no  such  thing 
as  great  and  small,  near  and  re- 
mote ;  relatively  speaking,  however, 
we  may  apply  the  terms,  great,  and 
very  great,  as  regards  both  mag- 
nitude and  distance.  Thus,  an  er- 
ror of  ten  feet  in  the  measure  of 
the  length  of  a  building,  is  very 
great  —  when  an  error  of  ten  rods, 
in  the  measure  of  one  hundred 
miles,  would  be  too  trifling  to 
mention. 

Now  if  we  consider  the  distance 
to  the  stars,  it  must  be  relative  to 
some  measure  taken  as  a  standard, 
or  our  inquiries  will  not  be  defi- 
nite, or  even  intelligible.  We  now 

Abstractly,  is  there  any  such  thing  as  great  and  small  ?  When  we  use 
the  term  great  or  small,  does  it  imply  a  standard,  of  measure  ?  Can  the 
same  amount  of  error  be  both  small  and  great  at  the  same  time. 


DISTANCES  OF  THE  HEAVENLY  BODIES.  69 

make  this  general  inquiry  :  Are  the  heavenly  bodies  near  to,  or 
remote  from,  the  earth?  Here,  the  earth  itself  seems  to  be  the 
natural  standard  for  measure  ;  and  if  any  body  were  but  two, 
three,  or  even  ten  times  the  diameter  of  the  earth,  in  distance, 
we  should  call  it  near;  if  100,  200,  or  2000  times  the  diameter 
of  the  earth,  we  should  call  it  remote.  To  answer  the  inquiry, 
Are  the  heavenly  bodies  near  or  remote?  we  must  put  them  to  all 
possible  mathematical  tests ;  a  mere  opinion  is  of  no  value, 
without  the  foundation  of  some  positive  knowledge.  Let  1,  2, 
represent  the  absolute  position  of  two  stars ;  and  then,  if  A  B 
C  represents  the  circumference  of  the  earth,  these  stars  may 
be  said  to  be  near;  but  if  a  be  represents  the  circumference 
of  the  earth,  the  stars  are  many  times  the  diameter  of  the 
earth,  in  distance,  and  therefore  may  be  said  to  be  remote.  If 
AEG  is  the  circumference  of  the  earth,  in  relation  to  these 
stars,  the  apparent  distance  of  the  two  stars  asunder,  as  seen 
from  Ay  is  measured  by  the  angle  1  A  2 ;  and  their  apparent 
distance  asunder,  as  seen  from  the  point  B,  is  measured  by  the 
angle  1  B  2;  and  when  the  circumference  ABC  is  very  large, 
as  represented  in  our  figure,  the  angle  A,  between  the  two 
stars,  is  manifestly  greater  than  B.  But  if  a  b  c  is  the  circum- 
ference of  the  earth,  the  points  a  and  b  are  relatively  the  same 
as  A  and  B.  And,  it  is  an  occular  demonstration  that  the  angle 
under  which  the  two  stars  would  appear  at  a  is  the  same,  or 
nearly  the  same,  as  that  under  which  they  would  appear  at  b; 
or,  at  least,  we  can  conceive  the  earth  so  small,  in  relation  to 
the  distance  to  the  stars,  that  the  angle  under  which  two  stars 
would  appear,  would  be  the  same,  seen  from  any  point  on  the 
earth. 

Conversely,  then,  if  the  angle  under  which  two  stars  appear 
is  the  same,  as  seen  from  all  parts  of  the  earth's  surface,  it  is 
certain  that  the  diameter  of  the  earth  is  very  small,  compared 
with  the  distance  to  the  stars;  or,  which  is  the  same  thing, 

To  measure  the  distances  to  the  heavenly  bodies  —  what  seems  to  be  the 
natural  standard  of  measure  ?  If  the  stars  appeared  at  different  distances 
asunder,  as  seen  from  different  parts  of  the  earth,  what  would  that  show  ? 


70  ELEMENTARY  ASTRONOMY. 

the  distance  to  the  stars  is  many  times  the  diameter  of  the  earth. 
Therefore,  observation  has  long  since  decided  this  important 
point.  Sir  John  Herschel  says:  "The  nicest  measurements 
of  the  apparent  angular  distance  of  any  two  stars,  inter  se, 
taken  in  any  parts  of  their  diurnal  course  (after  allowing  for 
the  unequal  effects  of  refraction,  or  when  taken  at  such  times 
that  this  cause  of  distortion  shall  act  equally  on  both),  mani- 
fest not  the  slightest  perceptible  variation.  Not  only  this,  but 
at  whatever  point  of  the  earth's  surface  the  measurement  is 
performed,  the  results  are  absolutely  identical.  No  instruments 
ever  yet  invented  by  man  are  delicate  enough  to  indicate,  by 
an  increase  or  diminution  of  the  angle  subtended,  that  one 
point  of  the  earth  is  nearer  to  or  farther  from  the  stars  than 
another." 

Perhaps   the   following  view  of   this  subject  will  be  more 
intelligible  to  the  general  reader. 

Let  Z  H  N 
H  represent  the 
celestial  equator, 
as  seen  from  the 
equator  on  the 
earth  ;  and  if  the 
earth  be  large, 
in  relation  to  the 
distance  to  the 
stars,  the  obser- 
ver will  be  at  z; 
and  the  part  of 
the  celestial  arc 
above  his  hori- 
zon would  be  represented  by  AZB,  and  the  part  below  his  ho- 
rizon by  ANBy  and  these  arcs  are  obviously  unequal ;  and 
their  relation  would  be  measured  by  the  time  a  star  or  heav- 
enly body  remains  above  the  horizon,  as  seen  from  the  equator, 

What  is  the  testimony  of  Sir  J.  Herschel  ?    What  do  we  infer  from  this 
fact  ?    What  other  illustration  is  given  ? 


HORIZONTAL  PARALLAX.  71 

compared  with  the  time  below  it ;  but  by  observation,  (refrac- 
tion being  allowed  for)  not  the  least  difference  is  to  be  discov- 
ered, and  the  stars  are  above  the  horizon  as  long  as  they  are 
below ;  which  shows  that  the  observer  is  not  at  z,  but  at  z, 
and  even  more  near  the  center ;  so  that  the  arc  AZJ3,  is  imper- 
ceptibly unequal  to  the  arc  HNH;  that  is,  they  are  equal  to 
each  other  ;  and  the  earth  is  comparatively  but  a  point,  in 
relation  to  the  distance  to  the  stars. 

This  fact  is  well  established,  as  applied  to  the  fixed  stars, 
sun  and  planets ;  but  with  the  moon  it  is  different:  that  body  is 
longer  below  the  horizon  than  above  it,  which  shows  that  its 
distance  from  the  earth  is  at  least  measurable. 

We  view  the  moon  from  the  earth,  and  it  appears  to  cover  a 
certain  portion  of  the  celestial  circle,  which  we  called  the 
moon's  apparent  diameter;  the  half  of  this  arc  is  called  the  semi- 
diameter.  Now  if  we  were  at  the  moon  to  look  down  upon  the 
earth,  the  semi-diameter  of  the  earth  would  apparently  cover  a 
certain  arc  in  the  heavens,  and  this  certain  arc  viewed  from 
the  moon  is  called  the  moon's 

HORIZONTAL    PARALLAX. 

We  place  these  two  words  into  one  line  to  make  them  con- 
spicuous, on  account  of  their  importance  in  astronomy. 

When  we  can  find  the  horizontal  parallax  of  any  heavenly 
body,  we  can  determine  the  distance  of  that  body  from  the 
earth,  as  we  shall  soon  explain. 

Parallax  is  the  difference  in  position,  of  any  body,  as  seen  from 
the  center  of  the  earth,  and  seen  from  its  surface. 

When  a  body  is  in  the  zenith  of  any  observer,  to  him  it  has 
no  parallax ;  for  he  sees  it  in  the  same  place  in  the  heavens,  as 
though  he  viewed  it  from  the  center  of  the  earth.  The  great- 
est possible  parallax  that  a  body  can  have,  takes  place  when 

As  seen  from  the  equator,  do  the  stars  remain  as  long  above  the  horizon 
as  below  it  ?  What  does  that  show  ?  Is  the  moon  observed  to  be  as  long 
above  the  horizon,  (after  refraction  is  allowed  for)  as  below  it  ?  What 
does  this  fact  show  ?  What  is  parallax  ?  When  a  body  is  in  the  zenith, 
has  it  any  parallax  ?  Why  ? 


72  ELEMENTARY  ASTRONOMY. 

the  body  is  in  the  horizon  of  the  observer ;  and  this  parallax  is 
called  horizontal  parallax.  Hereafter,  when  we  speak  of  the 
parallax  of  a  body,  horizontal  parallax  is  to  be  understood, 
unless  otherwise,  expressed. 

A  clear  and  summary  illustration  of  parallax  in  general,  is 
given  by  the  following  figure: 

Let  C  be  the 
center  of  the 
earth,  Z  the  ob- 
server, and  P, 
or  p,  the  posi- 
tion of  a  body. 
From  the  cen- 
ter of  the  earth, 
the  body  is  seen 
in  the  direction 
of  the  line  CP, 
or  Cp;  from  the 

observer  at  Z,  it  is  seen  in  the  direction  of  ZP,  or  Zp ;  and 
the  difference  in  direction,  of  these  two  lines,  is  parallax.  When 
P  is  in  the  zenith,  there  is  no  parallax  ;  when  P  is  in  the 
horizon,  the  angle  ZPC  is  then  greatest,  and  it  is  the  horizontal 
parallax. 

We  now  perceive  that  the  horizontal  parallax  of  any  body  is 
equal  to  the  apparent  semi-diameter  of  the  earth,  as  seen  from  the 
body.  The  greater  the  distance  to  the  body,  the  less  is  its 
horizontal  parallax ;  and  when  the  distance  is  so  great  that  the 
semi-diameter  of  the  earth  would  appear  only  as  a  point,  then 
the  body  has  no  parallax.  Conversely,  if  we  can  detect  no 
sensible  parallax,  we  know  that  the  body  must  be  at  a  vast 
distance  from  the  earth,  and  the  earth  itself  must  appear  as  a 
point  from  such  a  body,  if,  in  fact,  it  were  even  visible. 

What  is  the  position  of  a  heavenly  body  when  its  parallax  is  greatest  ? 
Why  is  parallax  then  called  horizontal  parallax  ?  When  the  distance  of  a 
body  from  the  earth  increases,  does  its  horizontal  parallax  increase  or 
decrease  ? 


HORIZONTAL  PARALLAX.  73 

Trigonometry  gives  the  relation  between  the  angles  and 
sides  of  every  conceivable  triangle ;  therefore,  we  know  all 
about  the  horizontal  triangle  ZCP,  when  we  know  CZ  and 
the  angles.*  It  is  obvious  that  the  less  the  angle  ZPC  the 
greater  must  be  the  distance  CP  ;  that  is,  the  less  the  hori- 
zontal parallax,  the  greater  is  the  distance,  and  the  difficulty, 
and  the  only  difficulty,  is  to  obtain  the  horizontal  parallax,  or 
the  angle  ZPC. 

The  horizontal  parallax  cannot  be  directly  observed,  by 
reason  of  the  great  amount,  and  irregularity  of  horizontal 
refraction ;  but  if  we  can  obtain  a  parallax  at  any  considerable 
altitude,  we  can  compute  the  horizontal  parallax  therefrom. 

The  fixed  stars  have  no  sensible  horizontal  parallax,  as  we 
have  frequently  mentioned  ;  and  the  parallax  of  the  sun  is  so 
small,  that  it  cannot  be  directly  observed;  the  moon  is  the 
only  celestial  body  that  comes  forward  and  presents  its  paral- 
lax ;  and  from  thence  we  know  that  the  moon  is  the  only  body 
that  is  within  a  moderate  distance  of  the  earth. 

That  the  moon  had  a  sensible  parallax,  was  known  to  the 
earliest  observers,  even  before  mathematical  instruments  were 
at  all  refined ;  but  to  decide  upon  its  exact  amount,  and  detect 

•Calling  the  horizontal  parallax  of  any  body  p,  and  the  radius  of  the 
earth  r,  and  the  distance  of  the  body  from  the  center  of  the  earth  x,  (the 
radius  of  the  table  always  R,  or  unity},  then,  by  trigonometry,  we  have, 

R    :    x    :  :    s'm.p     :    r. 


Therefore, 


/    R    \ 

( )r 

\sm.  .p/ 


From  this  equation  we  have  the  following  general  rule,  to  find  the  dis- 
tance to  any  celestial  body  : 

RULE.  —  Divide  the  radius  of  the  tables  by  the  sine  of  the  horizontal  paral- 
lax. Multiply  that  quotient  by  the  semi-diameter  of  the  earth,  and  the  product 
will  be  the  result. 

This  result  will,  of  course,  be  in  the  same  terms  of  linear  measure  as  the 
semi-diameter  of  the  earth  :  that  is,  if  r  is  in  feet,  the  result  will  be  in  feet ; 
if  r  is  in  miles,  the  result  will  be  in  miles,  etc. : 

Can  horizontal  parallax  be  directly  observed  ?     Have  the  fixed  stars  any 
sensible  parallax  ?    Why  have  they  none  ?    Was  the  moon's  parallax  seu- 
eible  to  early  observers  ? 
7 


74  ELEMENTARY  ASTRONOMY. 

its  variations,  required  the  combined  knowledge  and  observa- 
tions of  modern  astronomers. 

The  lunar  parallax  was  first  recognized  in  Europe,  and  in 
northern  countries,  by  that  luminary  appearing  to  describe  more 
than  a  semicircle'  south  of  the  equator,  and  less  than  a  simicircle 
north  of  that  line,  during  its  revolutions  among  the  stars,  and, 
on  an  average,  it  was  observed  to  be  a  longer  time  south,  than 
north  of  the  equator;  but  no  such  inequality  could  be  observed 
from  the  region  of  the  equator. 

Observers  at  the  south  of  the  equator,  observing  the  posi- 
tion of  the  moon,  see  it  for  a  longer  time  north  of  the  equator 
than  south  of  it ;  and,  to  them,  it  appears  to  describe  more  than  a 
semicircle  north  of  the  equator. 

Here  then,  we  have  observation  against  observation,  imless 
we  can  reconcile  them.  But  the  only  reconciliation  that  can 
be  made,  is  to  conclude  that  the  moon  is  really  as  long  in  one 
hemisphere  as  in  the  other,  and  the  observed  discrepancy  must 
arise  from  the  positions  of  the  observers ;  and  when  we  reflect 
that  parallax  must  always  depress  the  object,  and  throw  it 
farther  from  the  observer,  it  is  therefore  perfectly  clear  that  a 
northern  observer  should  see  the  moon  farther  to  the  south 
than  it  really  is,  and  a  southern  observer  see  the  same  body 
farther  north  than  its  true  position. 

To  find  the  amount  of  the  lunar  parallax  requires  the  con- 
currence of  two  observers.  They  should  be  near  the  same 
meridian,  and  as  far  apart,  in  respect  to  latitude,  as  possible ; 
and  every  circumstance  that  could  affect  the  result,  must  be 
known. 

The  two  most-  favorable  stations  are  Greenwich  (England) 
and  the  Cape  of  Good  Hope.  They  would  be  more  favorable 
if  they  were  on  the  same  meridian  ;  but  the  small  change  in 

By  what  observation  was  the  moon's  parallax  shown  ?  Does  the  moon, 
on  an  average,  appear  to  cross  the  equator  to  us,  just  at  the  time  it  really 
does  cross  the  equator?  Does  parallax  elevate  or  depress  the  object? 
How  many  observers  are  necessary  to  determine  lunar  parallax  ?  What 
two  stations  are  most  favorable,  and  why  ? 


HORIZONTAL   PARALLAX.  *7T, 

declination,  while  the  moon  is  passing  f  om  one  meridian  to 
the  other,  can  be  allowed  for ;  and  thus  the  two  observations 
are  reduced  to  the  same  meridian  aan  are  equivalent  to  being 
made  at  the  same  time. 

The  most  favorable  times  for  such  observations,  are  when 
the  inoon  is  near  her  greatest  declinations,  for  then  the*  change 
of  declination  is  extremely  slow. 

Let  A  represent  the  place  of 
the  Greenwich  observatory,  and 
B  the  station  at  the  Cape  of 
Good  Hope.  C  is  the  center  of 
the  earth,  and  Z  and  Z'  are  the 
zenith  points  of  the  observers. 
Let  M  be  the  position  of  the  moon, 
and  the  observer  at  A  will  see  it 
projected  on  the  sky  at  m! ',  and 
the  observer  at  B  will  see  it  pro- 
jected on  the  sky  at  m. 

Now  the  figure  ACBM  is  a 
quadrilateral ;  the  angle  A  CB  is 
known  by  the  latitudes  of  the  two 
observers  ;  the  angles  MA  0  and 
MEG  are  the  respective  zenith 
distances,  taken  from  180°. 

But  the  sum  of  all  the  angles 
of  any  quadrilateral  is  equal  to 
four  right  angles ;  and  hence  the 
angles  at  A,  C,  and  B,  being 
known,  the  parallactic  angle  at  M 
is  known. 

In  this  quadrilateral,  then,  we 
have  two  sides,  AC  and  CB,  and  all  the  angles;  and  this  is 
sufficient  for  the  most  ordinary  mathematician  to  decide  every 
particular  in  connection  with  it;  that  is,  we  can  find  AM,  MB, 

What  are  most  favorable  times  for  observations  ?  Why?  In  the  figure 
before  us,  how  is  the  angle  31,  delcrmiueil  ? 


76  ELEMENTARY  ASTROTOMY. 

and  finally  MC.  Now  MC  being  known,  the  horizontal  paral- 
lax can  be  computed,  for  it  is  but  a  function*  of  the  distance. 

The  result  of  such  observations,  taken  at  different  times, 
show  all  values  to  MC,  between  SSjW,  and  63TVg-;  taking  the 
semi-diameter  of  the  earth  as  unity. 

These  variations  are  regular  and  systematic,  both  as  to  time 
and  place,  in  the  heavens  ;  and  they  show,  without  further  in- 
vestigation, that  the  moon  does  not  go  round  the  earth  in  a 
circle,  or,  if  it  does,  the  earth  is  not  in  the  center  of  that 
circle. 

The  parallax  corresponding  to  these  extreme  distances,  are 
61'  29"  and  53'  50". 

When  the  moon  moves  round  to  that  part  of  her  orbit  which 
is  most  remote  from  the  earth,  it  is  said  to  be  in  apogee;  and, 
when  nearest  to  the  earth,  it  is  said  to  be  in  perigee.  The 
points  apogee  and  perigee,  mainly  opposite  to  each  other,  do 
not  keep  the  same  place  in  the  heavens,  but  gradually  move 
forward  in  the  same  direction  as  the  motion  of  the  moon,  and 
perform  a  revolution  in  a  little  less  than  nine  years. 

Many  times,  when  the  moon  comes  round  to  its  perigee,  we 
find  its  parallax  less  than  61'  29",  and,  at  the  opposite  apogee, 
greater  than  53'  50".  It  is  only  when  the  sun  is  in,  or  near  a 
line  with  the  lunar  perigee  and  apogee,  that  these  greatest  ex- 
tremes are  observed  to  happen ;  and  when  'the  sun  is  near  a 
right  angle  to  the  perigee  and  apogee,  then  the  moon  moves 
round  the  earth  in  an  orbit  near  a  circle  ;  and  thus,  by  observ- 
ing with  care  the  variation  of  the  moon's  parallax,  we  find 
that  its  orbit  is  a  revolving  ellipse,  of  variable  eccentricity. 

Because  the    moon's   distance    from  the    earth  is   variable, 

*Function  of  the  distance,  that  is,  horizontal  parallax  and  distances  are 
mathematically  and  invariably  connected,  as  expressed  in  the  following 
equation  in  which  p  is  the  parallax  and  x  the  distance  MC.  xs\n.p=r. 

How  is  it  known  that  the  moon's  distance  from  the  earth  is  visible  ? 
What  are  the  extreme  distances?  What  is  understood  by  apogee  and  by 
perigee?  What  is  the  figure  of  the  lunar  orbit?  Is  the  orbit  equally 
eccentric  at  all  times  ?  "When. is  the  orbit. nearest  a  circle  ? 


HORIZONTAL  PAEALLAX.  77 

therefore  there  must  be  a  mean  distance :  we  shall  show,  here- 
after, that  her  motion  is  variable;  therefore  there  is  a  mean 
motion  ;  and  as  the  eccentricity  is  variable,  there  is  a  mean 
eccentricity. 

The  mean  distance  is  60.26,  the  semi-diameter  of  the  earth, 
corresponding  to  the  parallax  of  57'  3". 

The  variations  in  the  moon's  real  distance  must  correspond  to 
apparent  variations  in  the  moon's  diameter;  and  if  the  moon,  or 
any  other  body,  should  have  no  variation  in  apparent  diameter, 
we  should  then  conclude  that  the  body  was  always  at  the  same 
distance  from  us. 

The  change,  in  apparent  diameter,  of  any  heavenly  body,  is 
numerically  proportional  to  its  real  change  in  distance. 

Now  if  the  moon  has  a  real  change  in  distance,  as  observa- 
tions show,  such  change  must  be  accompanied  with  apparent 
changes  in  the  moon's  diameter;  and,  by  directing  observa- 
tions to  this  particular,  we  find  a  perfect  correspondence ; 
showing  the  harmony  of  truth,  and  the  beauties  of  real 
science. 

We  have  several  times  mentioned  that  the  moon's  horizontal 
parallax  is  the  semi -diameter  of  the  earth,  as  seen  from  the 
moon ;  which  will  be  obvious  by  inspecting  the  following 
figure,  in  which  E  represents  the  semi-diameter  of  the  earth,  m 
the  semi -diameter  of  the  moon,  and  D  the  distance  between 
them.  The  angle  at  the  extremity  E,  takes  in  the  moon's  semi- 
diameter,  and 
the  like  ano-le 

O 

at  the  extrem- 
ity m  is  the 
moon's  hori- 
zontal parallax, 
or  the  earth's  semi-diameter, as  seen  from  the  moon. 

The  variations  of  these  two  angles  depend  on  the  same  cir- 
cumstance—  the  variation  of  the  distance  between  the  earth  and 

What  is  the  mean  distance  between  the  earth  and  the  moon  ?  How  i3 
the  change  in  the  moon's  distance  indicated  ?  Does  the  moon's  semi, 
diameter  and  horizontal  parallax  correspond,  in  all  their  variations  ? 


ELEMENTARY  ASTRONOMY. 

moon ;  and,  depending  on  one  and  the  same  cause,  they  must 
vary  in  just  the  same  proportion. 

When  the  moon's  horizontal  parallax  is  greatest,  the  moon's 
semi-diameter  is  greatest;  and,  when  least,  the  semi-diameter  is 
the  least ;  and  if  we  divide  the  tangent  of  the  semi-diameter  by 
the  tangent  of  its  horizontal  parallax,  we  shall  always  find  the 
same  quotient  (the  decimal  0.27293);  and  that  quotient  is  the 
ratio  between  the  real  diameter  of  the  earth  and  the  diameter 
of  the  moon.  Having  this  ratio,  and  the  diameter  of  the 
earth,  7912  miles,  we  can  compute  the  diameter  of  the  moon 
thus : 

7912X0.27293=2169.4  miles. 

As  spheres  are  to  each  other  in  proportion  to  the  cubes  of 
their  diameters,  therefore  the  bulk  (not  mass)  of  the  earth,  is 
to  that  of  the  moon,  as  1  to  ^V,  nearly. 

It  may  be  remarked,  by  every  one,  that  we  always  see  the 
same  face  of  the  moon ;  which  shows  that  she  must  roll  on  an 
axis, in  the  same  time  as  her  mean  revolution  about  the  earth ; 
for,  if  she  kept  her  surface  towards  the  same  pa*u  of  the 
heavens,  it  could  not  be  constantly  presented  to  the  earth, 
because,  to  her  view,  the  earth  revolves  round  the  moon,  the 
same  as  to  us  the  moon  revolves  round  the  earth;  and  the 
earth  presents  phases  to  the  moon,  as  the  moon  does  to  us, 
except  opposite  in  time,  because  the  two  bodies  are  opposite  in 
position.  When  we  have  new  moon,  the  lunarians  have  full 
earth ;  and  when  we  have  first  quarter,  they  have  last  quarter, 
etc.  The  moon  appears,  to  us,  about  half  a  degree  in  diam- 
eter ;  the  earth  appears,  to  them,  a  moon,  about  two  degrees  in 
diameter,  invariably  fixed  in  their  sky. 

The  moon  is  an  opake  body,  and  shines  only  by  reflecting 
the  light  of  the  sun,  but  its  phases,  its  peculiar  and  variable 
path  about  the  earth,  and  its  periods  of  revolution,  will  be  the 
Subject  of  a  future  chapter. 

What  is  the  ratio  between  the  diameter  of  the  earth  and  the  diameter  of 
the  moon  ?  What  is  the  ratio  between  their  masses,  and  how  is  it  deter- 
mined ?  What  is  the  appearance  of  the  earth  as  seen  from  the  moon  2 


I 

SOLAR   PARALLAX,  <fco.  79 

CHAPTER    II. 

SOLAR  PARALLAX  — DISTANCE  TO  THE    SUN  — CHANGES  OF 
THE  SEASONS  — CLIMATE,  <fcc. 

WE  have  seen  in  the  preceding  chapter,  that  the  horizontal 
parallax,  and  semi-diameter  of  any  body,  have  a  constant  rela- 
tion to  each  other,  and  as  we  can  distinctly  observe  the  diame- 
ter of  the  sun,  if  we  could  observe  his  horizontal  parallax  we 
could  then  obtain  the  diameter  of  the  sun,  by  the  following 
proportion: 
U's  hor.  par.  :  |jj  semidia.  :  :  diam,  of  earth  *,  diam.  of  Q. 

But  the  sun's  horizontal  parallax  is  too  small  to  be  detected 
by  any  common  means  of  observation ;  hence  it  remained  un- 
known, for  a  long  series  of  years,  although  many  ingenious 
methods  were  proposed  to  discover  it.  The  only  decision  that 
ancient  astronomers  could  make,  concerning  it,  was,  that  it  must 
be  less  than  20"  or  15"  of  arc  ;  for,  were  it  as  much  as  that 
quantity,  it  could  not  escape  observation. 

Now  let  us  suppose  that  the  sun's  horizontal  parallax  is  less 
than  20";  that  is,  the  apparent  semi-diameter  of  the  earth,  as 
seen  from  the  sun,  must  be  less  than  20";  but  the  semi-diameter 
of  the  sun  is  15'  56",  or  956";  therefore  the  sun  must  be  vastly 
larger  than  the  earth  —  by  at  least  48  times  its  diameter;  and 
the  bulk  of  the  earth  must  be,  to  that  of  the  sun,  fti  as  high  a 
ratio  as  1  to  the  cube  of  48.  But  as  at  present  we  do  not 
suffer  ourselves  to  know  the  true  horizontal  parallax  of  the 
sun,  all  the  decision  we  can  make  on  this  subject  is,  that  the 
sun  is  vastly  larger  than  the  earth. 

We  shall  now  call  to  mind  the  fact,  that  the  solar  day  is 
about  4  minutes  longer  than  the  sidereal  day,  which  shows  that 
the  sun  has  an  apparent  motion  eastward  among  the  stars, 

By  what  proportion  can  we  find  the  diameter  of  any  heavenly  body? 
Why  can  we  not  at  present  determine  the  diameter  of  the  sun  ? 


80  ELEMENTARY  ASTRONOMY. 

and  has  the  appearance  of  going  round  the  earth  once  in  a 
year :  but  the  appearance  would  be  the  same,  whether  the  earth 
revolves  round  the  sun,  or  the  sun  round  the  earth,  or  both 
bodies  revolve  round  a  point  between  them.  We  are  now  to 
consider  which  is  the  most  probable  :  that  a  large  body  should 
circulate  round  a  much  smaller  one;  or,  the  smaller  one  round  a 
larger  one.  The  last  suggestion  corresponds  with  our  know- 
ledge and  experience  in  mechanical  philosophy ;  the  first  is 
opposed  to  it. 

The  apparent  diameter  of  a  heavenly  body  can  be  measured 
by  the  time  it  occupies  in  passing  the  meridian  wire  of  a  transit 
instrument,  but  for  very  small  objects,  such  as  the  planets,  the 
use  of  a  micrometer  is  better.  A  micrometer  is  a  pair  of  parallel 
wires  near  the  focus  of  a  telescope,  which  open  and  close  by 
a  mathematical  contrivance,  and  the  amount  of  opening  is 
measured  by  the  turns  of  a  screw  from  the  closing  point, 
which  amount  determines  the  apparent  diameter  of  the  body. 

Observations  can  be  made  every  clear  day  through  the  year, 
to  determine  the  apparent  diameter  of  the  sun,  and  they  have 
been  made  at  many  places,  and  for  many  years;  and  the  com- 
bined results  show  that  the  apparent  diameter  of  the  sun  is 
the  same,  on  the  same  day  of  the  year,  from  whatever  station 
observed. 

The  least  semi-diameter  is  15'  45".  1  ;  which  corresponds,  in 
time,  to  the  first  or  second  day  of  July ;  and  the  greatest  is  16' 
17". 3,  which  takes  place  on  the  1st  or  2d  of  January. 

Now  as  we  cannot  suppose  that  there  is  any  real  change  in 
the  diameter  of  the  sun,  we  must  impute  this  apparent  change 
to  real  change  in  the  distance  of  the  body. 

Therefore  the  distance  to  the  sun  on  the  30th  of  December, 

How  do  we  know  that  the  sun  appears  to  move  round  the  earth  in  q 
year  ?  Does  the  sun  really  move,  or  is  it  the  earth  that  moves  ?  How  can 
we  measure  the  apparent  diameter  of  a  body  ?  What  is  a  micrometer, 
give  some  general  idea  of  one?  Is  the  apparent  diameter  of  the  sun 
always  the  same?  What  must  we  infer  from  this  fact?  When  is  the 
apparent  semi-diameter  least  ?  When  greatest  ?  Is  the  change  uniform 
and  gradual  ? 


SOLAR   PARALLAX,    <fcc.  rl 

must  be  to  its  distance  on  the  first  day  of  July,  as  the  number 
15'  45".  1  is  to  the  number  16'  17".3,  or  as  the  number  945.1  to 
977.3  ;  and  all  othef*  days  in  the  year,  the  proportional  distance 
must  be  represented  by  intermediate  numbers. 

From  this,  we  perceive  that  the  sun  must  go  round  the 
earth,  or  the  earth  round  the  sun,  in  very  nearly  a  circle;  for 
were  a  representation  of  the  curve  drawn,  corresponding  to  the 
apparent  semi-diameter  in  different  parts  of  the  orbit,  and 
placed  before  us,  the  eye  could  scarcely  detect  its  departure 
from  a  circle. 

It  should  be  observed,  that  the  time  elapsed  between  the 
greatest  and  least  apparent  diameter  of  the  sun,  or  the  reverse, 
is  just  half  a  year;  and  the  change  in  the  sun's  longitude  is 
180°. 

If  we  consider  the  mean  distance  between  the  earth  and 
sun  as  unity  (as  is  customary  with  astronomers),  and  then 
put  x  to  represent  the  least  distance,  and  y  the  greatest  dis- 
tance, we  shall  have 

#-)~y=2. 

And,     -     -    x     :    y     :  :     9451     :     9773. 

A  solution  gives  #=0. 98326,  nearly,  and  y=  1.0 1674,  nearly; 
showing  that  the  least,  mean  and  greatest  distance  to  the  sun, 
must  be  very  nearly  as  the  numbers  .98326,  1.,  and  1.01674. 

The  fractional  part,  (.01674,)  or  the  difference  between  the 
extremes  and  mean  (when  the  mean  is  unity),  is  called  the  eccen- 
tricity of  the  orbit. 

In  theory,  the  apparent  diameters  are  sufficient  to  determine 
the  eccentricity,  could  we  really  observe  them  to  rigorous 
exactness  ;  but  all  luminous  bodies  are  more  or  less  affected 
by  irradiation,  which  dilates  a  little  their  apparent  diameters ; 
and  the  exact  quantity  of  this  dilatation  is  not  yet  well  ascer- 
tained. 

How  great  is  the  elapsed  time  from  one  extreme  to  the  other  ?  What  is 
the  difference  in  the  sun's  longitude  ?  What  is  meant  by  the  eccentricity 
of  th«  earth's  orbit  ?  What  is  the  amount  of  the  eccentricity  ? 


82  ELEMENTARY  ASTRONOMY. 

The  eccentricity,  as  just  mentioned,  must  not  "be  regarded  as 
accurate.  It  is  only  a  first  approximation,  deduced  from  the 
first  and  most  simple  view  of  the  subject ;  when  we  obtain  full 
command  over  science,  we  can  find  methods  which,  with  less 
care,  will  give  more  accurate  results. 

The  sun's  right  ascension  and  declination  can  be  observed 
from  any  observatory,  any  clear  day,  and  from  thence  we  can 
trace  its  path  along  the  celestial  concave  sphere  above  us,  and 
determine,  its  change  from  day  to  day  ;  and  we  find  it  runs 
along  a  great  circle  called  the  ecliptic,  which  crosses  the  equa- 
tor at  opposite  points  in  the  heavens ;  and  the  ecliptic  inclines 
to  the  equator  with  an  angle  of  about  23°  27'  37". 

The  plane  of  the  ecliptic  passes  through  the  center  of  the 
earth,  showing  it  to  be  a  great  circle,  or  what  is  the  same 
thing,  showing  that  the  apparent  motion  qf  the  sun  has  its 
center  in  the  line  which  joins  the  earth  and  sun. 

The  apparent  motion  of  the  sun  along  the  ecliptic  is  called 
longitude ;  and  this  is,  its  most  regular  motion. 

When  we  compare  the  sun's  motion,  in  longitude,  with  its 
semi-diameter,  we  find  a  correspondence  — at  least,  an  apparent 
connection. 

When  the  semi-diameter  is  greatest,  the  motion  in  longitude 
is  greatest ;  and,  when  the  semi-diameter  is  least,  the  motion 
in  longitude  is  least;  but  the  two  variations  have  not  the  same 
ratio, 

When  the  sun  is  nearest  to  the  earth,  on  or  about  the  30th 
of  December,  it  changes  its  longitude,  in  a  mean  solar  day, 
1°  1'  9".95.  When  farthest  from  the  earth,  on  the  1st  of  July, 
its  change  of  longitude,  in  24  hours,  is  only  57'  11  ".48.  A 
uniform  motion,  for  the  whole  year,  is  found  to  be  59'  8".33. 

The  ancient   philosophers   contended   that  the   sun   moved 

What  is  understood  by  the  ecliptic  ?  How  can  that  circle  be  deter- 
mined ?  What  is  the  inclination  of  the  ecliptic  to  the  equator.  What 
connection  do  we  observe  between  the  sun's  semi-diameter,  and  its  motion 
in  longitude  ?  Do  they  both  increase  and  decrease  at  the  same  time,  and 
in  the  same  ratio  ? 


SOLAR    PARALLAX,  <fec.  83 

about  the  earth  in  a  circular  orbit,  and  its  real  velocity  uniform  ; 
but  the  earth  not  being  in  the  center  of  the  circle,  the  same  . 
portion  of  the  circle  would  appear  under  different  angles  ;  and 
hence  the  variation  in  the  sun's  apparent  angular  motion. 

Now  if  this  were  a  true  view  of  the  subject,  the  variation  in 
the  angular  motion  must  be  in  exact  proportion  to  the  variation 
in  distance  ;  that  is,  945".l  should  be  to  977".3  as  57'  H".48  to 
61'  9".95,  if  the  supposition  of  the  first  observers  were  true. 
But  these  numbers  have  not  the  same  ratio  ;  therefore  this  sup- 
position was  not  satisfactory  ;  and  it  was  probably  abandoned 
for  the  want  of  this  mathematical  support.  The  ratio  between 


945".l  and  977".3     ....      .lllf  =1.0341,  nearly; 

9451 

Between  57'  11".48  and  61'  9".95       3669/'--  =  1.0694,  nearly. 

343T.48 

If  we  square  (1.0341)  ihejirst  ratio,  we  shall  have  1.06936,  a 
number  so  near  in  value  to  the  second  ratio,  that  we  conclude 
it  ought  to  be  the  same,  and  would  be  the  same,  provided  we 
had  perfect  accuracy  in  the  observations. 

Thus  we  compare  the  angular  motion  of  the  sun  in  different 
parts  of  its  orbit  ;  and  we  always  find,  that  the  inverse  square  of 
its  distance  is  proportional  to  its  angular  motion  ;  and  this  incon- 
testable fact  is  so  exact  and  so  regular,  that  we  lay  it  down  as 
a  law  ;  and  if  solitary  observations  do  not  correspond  with  it, 
we  must  condemn  the  observations,  and  not  the  law. 

By  the  aid  of  a  little  geometry  in  connection  with  this  law,* 

*  By  making  use  of  this  law,  we  can  find  the  eccentricity  of  the  solar 
o"bit,  to  greater  precision  than  bv  the  apparent  diameters,  because  the  same 
error  of  observation  on  longitude  would  not  be  as  proportionally  great  as 
on  apparent  diameter. 

Let  E  be  the  eccentricity  of  the  orbit  ;  then  (1  —  E)  is  the  least  distance  to 
the  sun,  and  (I-}-/?;  the  greatest  distance.  Then,  by  observation,  we  have 

(\—E}*  :  (\+E)2  :  :  57'  11".48  :  61'9".95; 
Or,  (l—  E)2  :  (1-HO  '•-  343148  :  366995; 
Or,  \—E  :  \-{-E  :  :  J343148  :  J  366995. 

Whence  £=.016788-1-. 

What  law  exists  between  the  distance  of  the  sun  and  its  angular  motion  ? 
What  other  law  is  derive^  from  this  one  by  the  aid  of  geometry  ? 


84  ELEMENTARY  ASTRONOMY. 

it  is  easily  demonstrated  that  the  solar  radius  vector  describe* 
equal  areas  in  equal  times.  This  is  one  of  Kepler's  laws  that 
applies  to  all  the  planets,  and  it  is  capable  of  an  abstract  geo- 
metrical demonstration.  (See  page  163,  Univ.  Ed.) 

If  we  draw  lines  from  any  point  in  a  plane,  reciprocally  pro- 
portional to  the  sun's  apparent  diameter,  and  at  angles  differing 
as  the  change  of  the  sun's  longitude,  and  then  connect  tho 
extremities  of  such  lines  made  all  round  the  point,  the  con- 
necting lines  will  form  a  curve,  corresponding  with  an  ellipse, 
which  represents  the  apparent  solar  orbit ;  and,  from  a  review 
of  the  whole  subject,  we* give  the  following  summary  : 

1.  The  eccentricity  of  the  solar  ellipse,  as  determined  from  the 
apparent  diameter  of  the  sun,  is  .01674. 

2.  The  sun's  angular  velocity  varies  inversely  as  the  square  of 
its  distance  from  the  earth. 

3.  The  real  velocity  is  inversely  as  the  distance. 

4.  The  areas  described  by  the  radius  vector  are  proportional  to 
the  times  of  description. 

We  have  several  times  mentioned,  that,  as  far  as  appearances 
are  concerned,  it  is  immaterial  whether  we  consider  the  sun 
moving  round  the  earth,  or  the  earth  round  the  su^i ;  for,  if  the 

earth  is  in  one  position 
of  the  heavens,  the  sun 
will  appear  exactly 
in  the-opposite  position, 
and  every  motion  made 
by  the  earth  must  cor- 
respond to  an  apparent 
motion  made  by  the  sun. 
But  for  the  purpose 
of  being  nearer  to  fact, 
we  will  now  suppose  that  the  earth  revolves  round  the  sun  in  an 
elliptical  orbit,  as  represented  in  the  figure  in  the  margin. 

What  figure  will  represent  the  solar  orbit?    Would  appearances  be  the 
same,  whetber  the.  eartk  W9ve4  i'oun4  ^e-  sun,  or  the  sun  round  the  earth  ct 


SOLAR   PARALLAX,  Ao.  86 

We  have  very  much  exaggerated  the  eccentricity  of  the 
orbit,  for  the  purpose  of  bringing  principles  clearer  to  view. 

Tii.?  greatest  and  least  distances,  from  the  sun  to  the  earth, 
make  a  straight  line  through  the  sun,  and  cut  the  orbit  into  two 
equal  parts. 

When  the  earth  is  at  B,  the  sun  is  said  to  be  in  apogee,  or 
the  earth  is  said  to  be  in  its  aphelion  ;  when  the  earth  is  at  A, 
the  sun  is  said  to  be  in  perigee,  or  the  earth  is  said  to  be  in  itu 
perihelion. 

The  line  joining  these  two  points  is  the  major  diameter  of  the 
orbit ;  and  it  is  the  only  diameter  passing  through  the  sun,  that 
cuts  the  orbit  into  two  equal  parts. 

Now,  as  equal  areas  are  described  in  equal  times,  it  follows 
that  the  sun  must  be  just  half  a,  year  in  passing  from  apogee 
to  perigee,  and  from  perigee  to  apogee  ;  provided  that  these 
points  are  stationary  in  the  heavens,  and  they  are  so,  very 
nearly. 

If  we  suppose  the  earth  moves  along  the  orbit  from  D  to  A, 
and  we  observe  the  sun  from  D,  and  continue  observations 
upon  it  until  the  earth  comes  to  G,  then  the  longitude  of  the 
sun  has  changed  380°  ;  and  if  the  time  is  less  than  half  a  year, 
we  are  sure  tlw3  perigee  is  in  this  part  of  the  orbit.  If  we  con- 
tinue observations  round  and  round,  and  find  where  180°  of 
longitude  correspond  with  half  a  year,  there  will  be  the  posi- 
tion of  the  longer  axis  ;  which  is  sometimes  called  the  line  of 
the  apsides. 

By  this  method  the  position  of  the  longer  axis  is  more  accu- 
rately ascertained  than  it  could  be  by  observing  variations  in 
the  sun's  apparent  diameter,  because  the  variations  of  apparent 
diameter  are  quite  imperceptible,  for  several  degrees,  at  the 
extremities  of  the  major  axis. 

The  longitude  of  the  aphelion,  for  the  year   1801,  was  9(<r 
51'  9",  and  of  course,   the   perihelion   was   in  longitude   270° 

What  line,  passing  through  the  sun,  will  cut  the  orbit  of  the  earth  into 
two  equal  parts?  Does  the  sun  describe  180°  from  any  point  in  just  half 
a  year,  or  must  it  be  from  some  particular  point  ?  How  do  astronomers 
find  the  position  of  tka  major  axis?  What  was  the  position  of  it  in  1801? 


86  ELEMENTARY  ASTRONOMY. 

61'  9".  These  points  move  forward,  in  respect  to  the  stars, 
about  12"  annually,  and,  in  respect  to  the  equinox,  about  62"; 
more  exactly  61".905,  and,  of  course,  this  is  their  annual  in- 
crease of  longitude. 

In  the  year  1250,  the  perigee  of  the  sun  coincided  with  the 
winter  solstice,  and  the  apogee  with  the  summer  solstice ;  and 
at  that  time  the  sun  was  178  days  and  about  17-J-  hours  on  the 
south  side  of  the  equator,  and  186  days  and  about  12^-  hours 
on  the  north  side ;  being  longer  in  the  northern  hemisphere 
than  in  the  southern,  by  seven  days  and  19  hours.  At  present, 
the  excess  is  seven  days  and  near  17  hours. 

As  the  sun  is  a  longer  time  in  the  northern  than  in  the  south- 
ern "hemisphere,  the  first  impression  might  be,  that  more  solar 
heat  is  received  in  one  hemisphere  than  in  the  other;  but  the 
amount  is  the  same  ;  for  whatever  is  gained  in  time,  is  lost  in 
distance ;  and  what  is  lost  in  time,  is  gained  by  a  decrease  of 
distance.  The  amount  of  heat  depends  on  the  intensity  multi- 
plied by  the  time  it  is  applied  ;  and  the  product  of  the  time 
and  distance  to  the  sun,  is  the  same  in  either  hemisphere  ;  but 
the  amount  of  heat  received,  for  a  single  day,  is  different  in 
the  two  hemispheres. 

When  the  earth  is  at  B  and  at  A,  the  mean  and  true  longi- 
tude, of  the  sun  agree  ;  at  all  other  points  the  mean  place  of 
the  sun  is  not  the  same  as  its  true  place.  The  mean  place  can 
be  determined  by  the  time  from  the  apogee  or  perigee  points, 
and  the  true  place  can  be  determined  by  meridian  observations 
at  any  observatory.  The  difference  between  these  two  places 
is  noted  and  put  down  in  a  table  called  the  equation  of  the  sun's 
center.  The  equation  of  the  center  can  also  be  determined  by 
mathematical  computation  when  once  the  eccentricity  of  the 
ellipse  is  known. 

Are  there  different  degrees  of  heat  received  in  the  different  hemispheres 
during  the  year  ?  "What  does  the  amount  of  heat  depend  upon  ?  What  is 
meant  by  the  equation  of  the  sun's  center  ? 


THE  CAUSES  OF  THE  CHANGE  OF  SEASONS. 


87 


CHAPTER    III. 

• 

THE   CAUSES   OF    THE    CHANGE   OF   SEASONS. 

THE  annual  revolution  of  the  earth  in  its  orbit,  combined 
with  the  position  of  the  earth's  axis  to  the  plane  of  its  orbit, 
produces  the  change  of  the  seasons. 

If  the  axis  were  perpendicular  to  the  plane  of  its  orbit,  there 
would  be  no  change  of  seasons,  and  the  sun  would  then  be  all 
the  while  in  the  celestial  equator. 

This  will  be  understood  by  the  following  figure.  Conceive 
the  plane  of  the  paper  to  be  the  plane  of  the  earth's  orbit,  and 
conceive  the  several  representations  of  the  earth's  axis, 
to  be  inclined  to  the  paper  at  an  angle  of  66°  32'. 


In  all  representations  of  JVS,  one  half  of  it  is  supposed  to 
be  above  the  paper,  the  other  half  below  it. 

NS  is  always  parallel  to  itself;  that  is,  it  is  always  in  the 

What  produces  the  change  of 


88  ELEMENTARY  ASTRONOMY. 

same  position  —  always  at  the  same  inclination  to  the  plane  of 
its  orbit — always  directed  to  the  same  point  in  the  heavens, 
in  whatever  part  of  the  orbit  the  earth  may  be. 

The  plane  of  the  equator  represented  by  Eq,  is  inclined  to 
the  plane  of  the  orbit  by  an  angle  of  23°  28'. 

By  inspecting  the  figure,  the  reader  will  gather  a  clearei 
view  of  the  subject  than  by  whole  pages  of  description  :  he 
will  perceive  the  reason  why  the  sun  must  shine  over  the  north 
pole,  in  one  part  of  its  orbit,  and  fall  as  far  short  of  that  point 
when  in  the  opposite  part  of  its  orbit  ;  and  the  number  of  de- 
grees of  this  variation  depends,  of  course,  on  the  position  of 
the  axis  to  the  plane  of  the  orbit. 

Now  conceive  the  line  NS  to  stand  perpendicular  to  the 
plane  of  the  paper,  and  continue  so ;  then  Eq  would  lie  on  the 
paper,  and  the  sun  would  at  all  times  be  in  the  plane  of  the 
equator,  and  there  would  be  no  change  of  seasons.  If  N& 
were  more  inclined  from  the  perpendicular  than  it  now  is,  then 
we  should  have  a  greater  change  of  seasons. 

By  inspecting  the  figure,  we  perceive,  also,  that  when  it  is 
summer  in  the  northern  hemisphere,  it  is  winter  in  the  southern; 
and  conversely,  when  it  is  winter  in  the  northern,  it  is  summer 
in  the  southern. 

When  a  line  from  the  sun  makes  a  right  angle  with  the 
earth's  axis,  as  it  must  do  in  two  opposite  points  of  its  orbit, 
the  sun  will  shine  equally  on  both  poles,  and  it  is  then  in  the 
plane  of  the  equator;  which  gives  equal  days  and  nights  the 
world  over. 

Equal  days  and  nights,  for  all  places,  happen  on  the  20th  of 
March  of  each  year,  and  on  the  22d  or  23d  of  September.  At 
these  times  the  sun  crosses  the  celestial  equator,  and  it  is  said 
to  be  in  the  equinox. 

The  longitude  of  the  sun  at  the  vernal  equinox,  is  0°  ;  and 
at  the  autumnal  eqiiinox,  its  longitude  is  \  80°. 

What  is  the  inclination  of  the  earth's  axis  to  the  plane  of  its  orbit  ?  If 
the  inclination  were  90°,  would  there  be  any  change  of  seasons  ?  Does  the 
earth's  axis  always  keep  the  same  position  ?  How  do  we  ki>ow  that  ? 


THE  CAUSES  OF  THE  CHANGE  OF  SEASONS.      89 

The  time  of  the  greatest  north  declination  is  the  20th  of 
June  ;  the  sun's  longitude  is  then  90°,  and  is  said  to  be  at  the 
summer  solstice. 

The  time  of  the  greatest  south  declination  is  the  22d  of 
December ;  the  sun's  longitude,  at  that  .time,  is  270°,  and  is 
eaid  to  be  at  the  winter  solstice. 

By  inspecting  the  figure,  we  perceive,  that  when  the  earth 
is  at  the  summer  solstice,  the  north  pole,  P,  and  a  considera- 
ble portion  of  the  earth's  surface  around,  is  within  the  enlight- 
ened half  of  the  earth  ;  and  as  the  earth  revolves  on  its  axis 
JWS,  this  portion  constantly  remains  enlightened,  giving  a  con- 
stant day  — or  a  day  of  weeks  and  months  duration,  according 
as  any  particular  point  is  nearer,  or  more  remote  from  the  pole  : 
the  pole  itself  is  enlightened  full  six  months  in  the  year,  and 
the  circle  of  more  than  24  hours  constant  sunlight,  extends  to 
23°  28'  from  the  pole  (not  estimating  the  effects  of  refraction). 
On  the  other  hand,  the  opposite,  or  south  pole,  S,  is  in  a  long 
season  of  darkness,  from  which  it  can  be  relieved  only  by  the 
earth  changing*  position  in  its  orbit. 

"Now,  the  temperature  of  any  part  of  the  earth's  surface 
depends  mainly,  if  not  entirely,  on  its  exposure  to  the  sun's 
rays.  Whenever  the  sun  is  above  the  horizon  of  any  place, 
that  place  is  receiving  heat ;  when  below,  parting  with  it,  by 
the  process  called  radiation  ;  and  the  whole  quantities  received 
and  parted  with  in  the  year,  must  balance  each  other  at  every 
station,  or  the  equilibrium  of  temperature  would  not  be  sup- 
ported. Whenever,  then,  the  sun  remains  more  than  12  hours 
above  the  horizon  of  anj-  place,  and  less  beneath,  the  general 
temperature  of  that  place  will  be  above  the  average ;  when  the 
reverse,  below.  As  the  earth,  then,  moves  from  A  to  B,  the 
days  growing  longer,  and  the  nights  shorter,  in  the  northern 
hemisphere,  the  temperature  of  every  part  of  that  hemisphere 

When  does  the  sun  attain  its  greatest  northern  declination?    "When  its 
greatest  southern  declination?      Is  there  any  night  at  the  north  pole  while 
the  sun's  declination  is  north  ?     What  is  the  extent  of  constant  daylight 
from  the  pole  when  the  sun's  declination  is  18  degrees  north? 
8 


90  ELEMENTARY  ASTRONOMY. 

increases,  as  we  pass  from  spring  to  summer,  while  at  the  same 
time  the  reverse  is  going  on  in  the  southern  hemisphere.  As 
the  earth  passes  from  B  to  (7,  the  days  and  nights  again  ap- 
proach to  equality  —  the  excess  of  temperature  in  the  northern 
hemisphere,  above  the  mean  state,  grows  less,  as  well  as  its 
detect  in  the  southern  ;  and  at  the  autumnal  equinox,  C,  the 
mean  state,  is  once  more  attained.  From  thence  to  D,  and, 
finally  round  again  to  A,  all  the  same  phenomena,  it  is  obvious," 
must  ngain  occur,  but  reversed;  it  being  now  winter  in  the 
northern,  and  summer  in  the  southern,  hemisphere." 

The  inquiry  is  sometimes  made,  why  we  do  not  have  the 
warmest  weather  about  the  summer  solstice,  and  the  coldest 
weather  about  the  winter  solstice. 

This  would  be  the  case  if  the  sun  immediately  ceased  to 
give  extra  warmth,  on  arriving  at  the  summer  solstice  ;  but  if 
it  could  radiate  extra,  heat  to  warm  the  earth  three  weeks  before 
it  came  to  the  solstice,  it  would  give  the  same  extra  heat  three 
weeks  after;  and  the  northern  portion  of  the  earth  must  con- 
tinue to  increase  in  temperature  as  long  as  the'sun  continues 
to  radiate  more  than  its  medium  degree  of  heat  over  the  sur- 
face, at  any  particular  place.  Conversely,  the  whole  region  of 
country  continues  to  grow  cold  as  long  as  the  sun  radiates  less 

than  its  mean  annual  decree  of  heat  over  that  rep-ion.     The 

I 

medium  degree  of  heat,  for  the  whole  year,  and  for  all  places, 
of  course,  takes  place  when  the  sun  is  on  the  equator  ;  the 
average  temperature,  at  the  time  of  the  two  equinoxes.  The 
medium  degree  of  heat,  for  our  northern  summer,  considering 
only  two  seasons  in  the  year,  takes  plage  when  the  sun's  decli- 
nation is  about  12  degrees  north  ;  and  the  medium  degree  of 
heat,  for  winter,  takes  place  when  the  sun's  declination  is  about 
12  degrees  south ;  and  if  this  be  true,  the  heat  of  summer  will 
begin  to  decrease  about  the  20th  of  August,  and  the  cold  of 

Why  is  not  the  20th  of  June  considered  as  mid-summer  in  the 
northern  hemisphere,  —  or,  rather,  why  is  July  the  mid-summer  season, 
and  not  June  ?  At  what  time  may  we  expect  the  seventy  of  winter  to 
be  past  V 


THE  CAUSES  OF  THE  CHANGE  OF  SEASONS.     91 

winter  must  essentially  abate,  on,  or  about,  the  16th  of  Febru- 
ary, in  all  northern  latitudes. 

The  warmest  part  of  the  day,  (other  circumstances  being 
equal,)  is  not  at  12,  but  about  2  o'clock  in  the  afternoon.  The 
sun  is  then  west  of  the  meridian,  and  its  rays  will  strike  more 
perpendicularly  on  a  plane  whose  downward  slope  is  towards 
the  west,  than  on  one,  whose  downward  slope  is  towards  the 
east. 

This  will  account  for  the  fact,  that  climates  are  more  mild 
west  of  mountain  ranges  than  on  the  eastern  side  of  the  same 
mountains,  other  circumstances  being  equal.  The  vicinity  of 
large  bodies  of  water,  and  the  general  elevation  of  the  country 
above  the  level  of  the  sea,  have  much  to  do  with  climate,  but 
as  these  causes  have  no  particular  connection  with  astronomy, 
we  omit  them. 

"What  time  of  day  is  warmest  ?  Why  not  at  noon  ?  Which  locality  has 
the  warmest  climate,  on  the  east  or  west  side  of  the  Alleghany  mountains, 
in  the  same  latitude  and  at  the  same  elevation  above  the  sea  1 


92  ELEMENTARY  ASTRONOMY. 

CHAPTER  IV. 
EQUATION   OF   TIME. 

WE  now  come  to  one  of  the  most  important  subjects  in 
astronomy  —  the  equation  of  time. 

Without  a  good  knowledge  of  this  subject,  there  will  be 
constant  confusion  in  the  minds  of  the  pupils  ;  and  such  is  the 
mature  of  the  case,  that  it  is  difficult  to  understand  even  the 
facts,  without  investigating  their  causes. 

Sidereal  time  has  no  equation  ;  it  is  uniform,  and,  of  itself, 
perfect  and  complete. 

The  time,  by  a  perfect  clock,  is  theoretically  perfect  and 
Complete,  and  it  is  called  mean  solar  time. 

The  time,  by  the  sun,  is  not  uniform  ;  and,  to  make  it  agree 
with  the  perfect  clock,  requires  a  correction  —  a  quantity  to 
make  equality  ;  and  this  quantity  is  called  the  equation  of 


If  the  sun  were  stationary  in  the  heavens,  like  a  star,  it 
come  to  the  meridian  after  exact  and  equal  intervals 
^f  time  ;  and,  in  that  case,  there  would  be  no  equation  of 
time. 

If  the  sun's  motion,  in  right  ascension,  were  uniform,  then 
it  would  also  come  to  the  meridian  after  equal  intervals  of 
time,  and  there  would  still  be  no  equation  of  time.  But 
(speaking  in  relation  to  appearances)  the  sun  is  not  stationary 
in  the  heavens,  nor  does  it  move  uniformly  ;  therefore  it  can- 
not come  to  the  meridian  at  equal  intervals  of  time,  and,  of 
course,  the  solar  days  must  be  slightly  unequal. 

*  In  astronomy,  the  term  equation,  is  applied  to  all  corrections,  to  con- 
vert a  mean  to  its  true  quantity. 

Are  all  sidereal  days  alike  in  length?  Are  all  solar  days  alike  in 
length  ?  If  solar  days  are  unequal  in  length,  what  will  it  produce  ? 


EQUATION  OF  TIME.  93 

When  the  sun  is  on  the  meridian,  it  is  then  apparent  noon 
for  that  day  :  it  is  the  real  solar  noon,  or,  the  half  elapsed  time 
between  sunrise  and  sunset. 

A  fixed  star  comes  to  the  meridian  at  the  expiration  of  every 
23h.  56m.  04.09s.  of  mean  solar  time ;  and  if  the  sun  were 
stationary  in  the  heavens,  it  \vould  come  to  the  meridian  after 
every  expiration  of  just  that  same  interval.  But  the  sun  in- 
creases its  right  ascension  every  day,  by  its  apparent  eastward 
motion  ;  and  this  increases  the  time  of  its  coming  to  the  meri- 
dian ;  and  the  mean  interval  between  its  successive  transits 
over  the  meridian  is  just  24  hours  ;  but  the  actual  intervals 
are  variable  —  some  less,  and  some  more,  than  24  hours. 

On  and  about  the  1st  of  April,  the  time  from  one  meridian 
of  the  sun  to  another,  as  measured  by  a  perfect  clock,  is  23h. 
69m.  52.4s. ;  less  than  24  hours  by  about  8  seconds.  Here, 
then,  the  sun  and  clock  must  be  constantly  separating.  On 
and  about  the  20th  of  December,  the  time  from  one  meridian 
of  the  sun  to  another  is  24h.  Om.  24.2s.,  more  than  24  seconds 
over  24  hours  ;  and  the  daily  accumulation  of  a  few  seconds 
will  soon  amount  to  minutes  —  and  thus  the  sun  and  clock  will 
become  very  sensibly  separated  —  and  this  is  the  equation  of 
time. 

To  detect  the  law  which  separates  the  sun  and  clock,  and 
find  the  amount  of  separation  for  any  particular  day,  we  must 
consider 

1st.     The  unequal  apparent  motion  of  the  sun  along  the  ecliptic. 

2d.      The  variable  inclination  of  this  motion  to  the  equator. 

If  the  sun's  apparent  motion  along  the  ecliptic  were  uniform, 
still  there  would  be  an  equation  of  time  ;  for  that  motion,  in 
some  parts  of  the  orbit,  is  oblique  to  the  equator,  and,  in  other 
parts,  parallel  with  it;  and  its  eastward  motion,  in  right  ascen- 
sion, would  be  greatest  when  moving  parallel  with  the  equator. 

When  is  it  apparent  noon?  When  is  it  mean  noon?  The  difference 
between  these  two  noon's  is  always  equal  to  what  ?  If  the  sun's  apparent 
motion  along  the  ecliptic  were  uniform,  would  there  still  be  an  equation 
of  time,  and  why  ? 


94  ELEMENTARY  ASTRONOMY. 

From  the  first  cause,  separately  considered,  the  sun  and 
clock  would  agree  two  days  in  a  year  —  the  1st  of  July  and  the 
30th  of  December. 

From  he  second  cause,  separately  considered,  the  sun  and 
clock  agree  four  days  in  a  year  —  the  days  when  the  sun 
crosses  the  equator,  and  the  days  he  reaches  the  solsticial 
points. 

When  the  results  of  these  two  causes  are  combined,  the  sun 
and  clock  will  agree  four  days  in  the  year ;  but  it  is  on  neither 
of  those  days  marked  out  by  the  separate  causes ;  and  the 
intervals  between  the  several  periods,  and  the  amount  of  the 
equation,  appear  to  want  regularity  and  symmetry. 

The  four  days  in  the  year  on  which  the  sun  and  clock  agree, 
that  is,  show  noon  at  the  same  instant,  are  April  15th,  June 
16th,  September  1st,  and  December  24th. 

The  elliptical  form  of  the  earth's  orbit  gives  rise  to  the  une- 
qual motion  of  the  earth  in  its  orbit,  and  thence  to  the  appa- 
rent unequal  motion  of  the  sun  in  the  ecliptic ;  and  this  same 
unequal  motion  is  what  we  have  denominated  the  first  cause  of 
the  equation  of  time.  Indeed,  this  part  of  the  equation  of 
time  is  nothing  more  than  the  equation  of  the  sun's  center, 
changed  into  time,  at  the  rate  of  four  minutes  to  a  degree. 

The  greatest  equation  for  the  sun's  longitude,  is  by  obser- 
vation 1°  55'  30";  and  this,  proportioned  into  time,  gives  7m. 
42s.  for  the  maximum  effect  in  the  equation  of  time  arising 
from  the  sun's  unequal  motion.  When  the  sun  departs  from 
its  perigee,  its  motion  is  greater  than  the  mean  rate,  and,  of 
course,  comes  to  the  meridian  later  than  it  otherwise  would. 
In  such  cases,  the  sun  is  said  to  be  slow  —  and  it  is  slow  all 
the  way  from  its  perigee  to  its  apogee  ;  and  fast  hi  the  other 
half  of  its  orbit. 

On  what  days  in  the  year  would  the  sun  and  clock  agree,  if  the  sun's 
motion  were  uniform  along  the  ecliptic?  On  what  days  in  the  year  do 
the  sun  and  clock  agree  ?  What  is  the  maximum  effect  for  the  sun's  une- 
qual motion  ? 


EQUATION  OF  TIME.  95 

For  a  more  particular  explanation  of  the  second  cause,  we 
must  call  attention  to  the  figure  in  the  margin. 

Let  Y*  @  LQJ  represent  the  ecliptic,  and  rp  C  LQJ  the 
equator. 

By  the  first  correc- 
tion, the  apparent  mo- 
tion along  the  ecliptic  is 
rendered  uniform ;  and 
the  sun  is  then  supposed 
to  pass  over  equal  spaces 
in  equal  intervals  of 
time  along  the  arc  ^  S 
@.  But  equal  spaces 
of  arc,  on  the  ecliptic, 
do  not  include  the  same 
meridians,  as  equal  spa- 
ces on  the  equator.  In 
short,  the  points  on  the 

ecliptic  must  be  reduced  to  corresponding  points  on  the  equator. 
For  instance,  the  number  of  degrees  represented  by  ^  $on  the 
ecliptic,  is  greater  than  to  the  same  meridian  along  the  equator. 
The  difference  between  'Y1  S  and  °p  Sf,  turned  into  time,  is  the 
equation  of  time  arising  from  the  obliquity  of  the  ecliptic  cor- 
responding to  the  point  S. 

At  the  points  'Y1,  69,  and  LQJ,  and  also  at  the  southern  tropic, 
the  ecliptic  and  the  equator  correspond  to  the  same  meridian ; 
but  all  other  equal  distances,  on  the  ecliptic  and  equator,  are 
included  by  different  meridians. 

It  will  be  observed,  by  inspecting  the  figure,  that  what  the 
sun  loses  in  eastward  motion,  by  oblique  direction  near  the  equa- 
tor, is  made  up,  when  near  the  tropics,  by  the  diminished  dis- 
tances between  the  meridians. 

For  a  more  definite  understanding  of  this  matter,  we  give 
the  folloAving  table  : 

When  does  the  sun  lose  most  in  eastward  motion  on  the  ecliptic  ? 
When  does  it  gain  most  in  eastward  motion  ? 


96  ELEMENTARY  ASTRONOMY. 

Table  showing  the  separate  results  of  the  two  causes  for  the  equa- 
tion of  time,  corresponding  to  every  fifth  day  of  the  second  years 
after  leap  year ;  but  is  nearly  correct  for  any  year. 


1st  cau*e. 
Bun    slow 
of  Clock. 

2d  cause. 
Sun  slow 
of  Clock. 

1st  cause 
fvn  fast. 

2d  cause. 
Sun  fast. 

m.  s. 

m.  s. 

m.  8. 

m.  s. 

January    5 

0  41 

5     8 

July           1 

0     0 

3  32 

10 

1  22 

6  35 

7 

0  40 

5     8 

15 

2    2 

7  48 

12 

1  19 

6  35 

20 

2  41 

8  45 

17 

1  57 

7  48 

25 

3  19 

9  26 

22 

2  35 

8  45 

29 

3  56 

9  49 

28 

3  12 

9  26 

February  3 

4  30 

9  53 

August      2 

3  47 

9  49 

8 

5    2 

9  40 

7 

4  21 

9  53 

13 

5  32 

9     9 

12 

4  52 

9  40 

18 

5  39 

8  23 

17 

5  22 

9     9 

23 

6  24 

7  22 

22 

5  50 

8  23 

28 

6  45 

6    9 

28 

6  14 

7  22 

March        5        7     3 

4  46 

Sept.          2 

6  36 

6    9 

10 

7  18 

3  15 

7 

6  56 

4  46 

15 

7  29 

1  39 

12 

7  12 

3  15 

20 

7  37 

sun  fast. 

17 

7  24 

1  39 

25 

7  42 

1  39 

23 

7  34 

sun  fast. 

30 

7  42 

3  15 

28 

7  40 

1  39 

April         4 

7  40 

4  46 

October      3 

7  42 

3  15 

9 

7  34 

6    9 

8 

7  40 

4  46 

14 

7  24 

7  22 

13 

7  34 

6     9 

19 

7  12 

8  23 

18 

7  24 

7  22 

24 

6  56 

9     9 

23 

7  12 

8  23 

30 

6  36 

9  40 

28 

6  56 

9    9 

May          5 

6  14 

9  53 

Nov.          2 

6  36 

9  40 

10 

5  50 

9  49 

7 

6  14 

9  53 

15 

5  22 

9  26 

12 

5  50 

9  49 

20 

4  52 

8  45 

17 

5  22 

9  26 

26 

4  21 

7  48 

22 

4  52 

8  45 

31 

3  47 

6  35 

27 

4  22 

7  48 

June          5 

3  12 

5     8 

Dec.           2 

3  47 

6  35 

10 

2  35 

3  32 

7 

3  12 

5    8 

16 

1  57 

1  48 

12 

2  35 

3  32 

21 

1  19 

sun  slow 

17 

1  57 

1  48 

26 

0  40 

1  48 

21 

1  19 

sun  slow 

26 

0  40        1  48 

By  this  table,  the  regular  and  symmetrical  result  of  each 
cause  is  visible  to  the  eye  ;  but  the  actual  value  of  the  equa- 
tion of  time,  for  any  particular  day,  is  the  combined  results 


What  is  the  first  cause  of  the  equation  of  time  ?    What  is  the  second 
cause? 


EQUATION   OF   TIME.  97 

of  these  two  causes.     Thus,  to  find  the  equation  of  time  for 
the  5th  day  of  March,  we  look  in  the  table  and  find  that 

The  first  cause  gives  sun  slow     -         -         7m.  3s. 

The  second  "     sun  slow         -  4     46 


Their  combined  result  (or  algebraic  sum)  is  11     49  slow. 

That  is,  the  sun  being  slow,  it  does  not  come  to  the  meridian 
until  llm.  49s.  after  the  noon  shown  by  a  perfect  clock  ;  but 
whenever  the  sun  is  on  the  meridian,  it  is  then  noon,  apparent 
time  ;  and,  to  convert  this  into  mean  time,  or  to  set  the  clock, 
we  must  add  llm.  49s. 

By  inspecting  the  table,  we  perceive  that  on  the  1 4th  of 
April  the  two  results  nearly  counteract  each  other  ;  and  conse- 
quently the  sun  and  clock  nearly  agree,  and  indicate  noon  at 
the  same  instant.  On  the  2d  of  November  the  two  results 
unite  in  making  the  sun  fast;  and  the  equation  of  time  is  thep 
the  sum  of  6  36  and  9  40,  or  16m.  16s. ;  the  maximum  result. 

The  sun  at  this  time  being  fast,  shows  that  it  comes  to  the 
meridian  16m.  16s.  before  12  o'clock,  true  mean  time;  or, 
when  the  sun  is  on  the  meridian,  the  clock  ought  to  show  llh. 
43m.  44s.  ;  and  thus,  generally,  when  the  sun  is  fast,  we  must 
subtract  the  equation  of  time  from  apparent  time,  to  obtain  mean 
time;  and  add,  when  the  sun  is  slow. 

As  no  clock  can  be  relied  upon,  to  run  to  true  mean  time, 
or  to  any  exact  definite  rate,  therefore  clocks  must  be  frequently 
rectified  by  the  sun.  We  can  observe  the  apparent  time,  and 
then,  by  the  application  of  the  equation  of  time,  we  determine 
the  true  mean  time. 

A  table  for  the  equation  of  time,  corresponding  to  each 
degree  of  the  sun's  longitude,  is  to  be  found  in  many  astro- 
nomical works,  and  such  a  table  would  be  perpetual,  provided 
the  longer  axis  of  the  solar  orbit  did  not  change  its  position  in 
relation  to  the  equinox.  But  as  that  change  is  very  slow,  a 

When  is  the  sun  said  to  be  slow  ?    When  fast  ?   Can  any  clock  be  relied 
upon  to  run  to  mean  time  ?    How  then  is  mean  time  discovered  ?    "W  hy  can 
we  not  have  a  perpetual  table  for  the  equation  of  time? 
9 


98  ELEMENTARY  ASTRONOMY. 

table  of  that  kind  will  serve  for  many  years,  with  a  trifling 
correction. 

We  repeat,  sidereal  time  is  the  interval  of  time  elapsed  since 
the  equinoctial  point  in  the  heavens  passed  the  meridian. 

The  solar  day  is  3m.  56s. 55  of  sidereal  time,  longer  than  a 
sidereal  day. 

At  the  instant  of  mean  noon,  Greenwich  time,  on  the  1st  of 

March,  1857,  the  sidereal  time  was 

h.       m.       s. 
Estimated  at         -         -         -         -         22     36     56.65 

To  this  add     -       :-         -  3     56.55 


Sidereal  time  at  noon,  March  2d,  22     40     53.20 

Thus  we  might  compute  the  sidereal  time  at  mean  noon, 
Greenwich  time,  for  any  number  of  days,  (omitting  24h.  when 
we  passed  that  sum.) 

At  mean  noon,  the  right  ascension  of  the  sun,  plus  or  minus 
the  equation  of  time,  is  always  equal  to  the  sidereal  time. 

Twenty -four  hours  of  mean  solar  time  is  equal  to  24h.  3m. 
56s. 55  of  sidereal  time.  Therefore  eight  hours  of  solar  time  is 
equal  to  8h.  1m.  18s. 82  of  sidereal  time  ;  and  thus  we  may 
correct  any  hour  of  solar  time  to  its  corresponding  value  of 
sidereal  time. 

On  the    1st  day  of  May,  1857,  at  mean  noon, 

h.    m.      s. 

The  sidereal  time  was        -        -        -     2     37     26.46 

Add, 81     18.82 


Sidereal  time  at  8,  mean  time,       -         10     38     45.28 
Thus  we  might  find  the  sidereal  time  corresponding  to  any 

other  hour,   on  any  other  day,  having  the  use  of  a  Nautical 

Almanac. 

It  is  very  important  that  the  navigator,  astronomer,  and  chcA 

regulator,  should  thoroughly  understand  the  equation  of  time ; 

and  persons  thus  occupied  pay  great  attention  to  it ;  but  most 

people  in  common  life  are  hardly  aware  of  its  existence. 

To  whom  is  equation  of  time  important  ? 


APPARENT   MOTIONS  OF   THE  PLANETS.  99 

CHAPTER    V. 
THE    APPARENT   MOTIONS    OF    THE  PLANETS. 

WE  have  often  reminded  the  reader  of  the  great  regularity 
of  the  fixed  stars,  and  of  their  uniform  positions  in  relation  to 
each  other ;  and  by  this  very  regularity  and  constancy  of  rela- 
tive positions,  we  denominate  them  fixed ;  but  there  are  certain 
other  celestial  bodies,  that  manifestly  change  their  positions 
in  space,  and,  among  them,  the  sun  and  moon  are  most  prom- 
inent. 

In  previous  chapters,  we  have  examined  some  facts  con- 
cerning the  sun  and  moon,  which  we  briefly  recapitulate,  as 
follows  : 

1.  That  the  sun's  distance  from  the  earth  is  very  great;  but 
at  present  we  cannot  determine  how  great,  for  the  want  of  one 
element  —  its  horizontal  parallax. 

2.  Its  magnitude  is  much  greater  than  that  of  the  earth. 

3.  The  distance  between  the  sun  and  earth  is  slightly  varia- 
ble ;  but  it  is  regular  in  its  variations,  both  in  distance  and  in 
apparent  angular  motion. 

4.  The   moon    is  comparatively  very   near  the    earth ;    its 
distance  is  variable,  and  its   mean  distance    and  amount  of 
variations  are  known.     It  is  smaller  than  the  earth,  although, 
to  the  mere  vision,  it  appears  as  large  as  the  sun. 

The  apparent  motions  of  both  sun  and  moon  are  always  in 
one  direction  ;  and  the  variations  of  their  motions  are  never 
far  above  or  below  the  mean. 

But  there  are  several  other  bodies  that  are  not  fixed  stars  ; 
and  although  not  as  conspicuous  as  the  sun  and  moon,  have 
been  known  from  time  immemorial. 

What  is  repeated  in  chapter  v.  concerning  the  fixed  stars  ?  What  is 
mentioned  again  concerning  the  sun  ?  What  in  relation  to  the  moon  ? 


100          ELEMENTARY  ASTRONOMY. 

They  appear  to  belong  to  one  family ;  but,  before  the  true 
system  of  the  world  was  discovered,  it  was  impossible  to  give 
any  rational  theory  concerning  their  motions,  so  irregular  and 
erratic  did  they  appear  ;  and  this  very  irregularity  of  their 
apparent  motions  induced  us  to  delay  our  investigations  con- 
cerning them  to  the  present  chapter. 

In  general  terms,  these  bodies  are  called  planets  —  and  there 
are  several  of  recent  discovery  —  and  some  of  very  recent 
discovery ;  but  as  these  are  not  conspicuous,  nor  well  known, 
all  our  investigations  of  principles  will  refer  to  the  larger 
planets,  Venus,  Mars,  Jupiter,  and  Saturn.  We  now  com- 
mence giving  some  observed  facts,  as  extracted  from  the  Cam- 
bridge astronomy. 

"  There  are  few  who  have  not  observed  a  beautiful  star  in 
the  west,  a  little  after  sunset,  and  called,  for  this  reason,  the 
evening  star.  This  star  is  Venus.  If  we  observe  it  for  several 
days,  we  find  that  it  does  not  remain  constantly  at  the  same 
distance  from  the  sun.  It  departs  to  a  certain  distance,  which 
is  about  45°,  or  {th  of  the  celestial  hemisphere,  after  which  it 
begins  to  return  ;  and  as  we  can  ordinarily  discern  it  with  the 
naked  eye  only  when  the  sun  is  below  the  horizon,  it  is  visible 
only  for  a  certain  time  immediately  after  sunset.  Subsequently 
it  sets  with  the  sun,  and  then  we  are  entirely  prevented  from 
seeing  it  by  the  sun's  light.  But  after  a  few  days,  we  perceive 
in  the  morning,  near  the  eastern  horizon,  a  bright  star  which 
was  not  visible  before.  It  is  seen  at  first  only  a  few  minutes 
before  sunrise,  and  is  hence  called  the  morning  star.  It  departs 
from  the  sun  from  day  to  day,  and  precedes  its  rising  more  and 
more  ;  but  after  departing  to  about  45°,  it  begins  to  return, 
and  rises  later  each  day  ;  at  length  it  rises  with  the  sun,  and 
we  cease  to  distinguish  it.  In  a  few  days  the  evening  star 
again  appears  in  the  west,  very  near  the  sun  ;  from  which  it 
departs  in  the  same  manner  as  before  ;  again  returns;  disap- 

What  bodies  are  planets  ?  In  what  respects  do  their  motions  differ  from 
the  fixed  stars  ?  Why  has  the  author  delayed  mentioning  these  bodies 
until  now  ?  What  planet  is  called  the  morning  and  evening  star  ? 


APPARENT   MOTIONS  OF  THE  PLANETS.  101 

pears  for  a  short  time  ;  and  then,  the  morning  star  presents 
itself. 

These  alternations,  observed  without  interruption  for  more 
than  2000  years,  evidently  indicate  that  the  evening  and  morn- 
ing- star  are  one  and  the  same  body.  They  indicate,  also,  that 
this  star  has  a  proper  motion,  in  virtue  of  which  it  oscillates 
about  the  sun,  sometimes  preceding  and  sometimes  following  it. 

These  are  the  phenomena  exhibited  to  the  naked  eye ;  but 
the  admirable  invention  of  the  telescope  enables  us  to  carry 
our  observations  much  farther." 

On  observing  Venus  with  a  telescope,  the  irradiation  is,  in  a 
great  measure,  taken  away,  and  we  perceive  that  it  has  phases, 
like  the  moon.  At  evening,  when  approaching  the  sun,  it  pre- 
sents a  luminous  crescent,  the  points  of  which  are  from  the 
sun.  The  crescent  diminishes  as  the  planet  draws  nearer  the 
sun  ;  but  after  it  has  passed  the  sun,  and  appears  on  the  other 
side,  the  crescent  is  turned  in  the  other  direction ;  the  enlight- 
ened part  always  toward  the  sun,  showing  that  it  receives  its 
light  from  that  great  luminary.  The  crescent  now  gradually 
increases  to  a  semicircle,  and  finally,  to  a  full  circle,  as  the 
planet  again  approaches  the  sun ;  but,  as  the  crescent  increases, 
the  apparent  diameter  of  the  planet  diminishes;  and  at  every 
alternate  approach  of  the  planet  to  the  sun,  the  phase  of  the 
planet  is  full,  and  the  apparent  diameter  small;  and  at  the 
other  approaches  to  the  sun,  the  crescent  diminishes  down  to 
zero,  and  the  apparent  diameter  increases  to  its  maximum. 
When  very  near  the  sun,  however,  the  planet  is  lost  in  the 
sunlight;  but  at  some  of  these  intervals,  between  disappearing 
in  the  evening  and  reappearing  in  the  morning,  it  appears  to 
run  over  the  sun's  disc  as  a  round,  black  spot ;  giving  a  fine 
opportunity  to  measure  its  greatest  apparent  diameter.  When 
Venus  appears  full,  its  apparent  diameter  is  not  more  than  10", 
and  when  a  black  spot  on  the  sun,  it  is  59". 8,  or  very  nearly  1'. 

How  do  we  know  that  the  morning  and  evening  star  must  be  the  same 
body  ?  What  is  the  appearance  of  the  planet  when  viewed  through  a  tel- 
escope ?  How  does  it  appear  that  Veuus  receives  its  light  from  the  sun  1 


102          ELEMENTARY  ASTRONOMY. 

Hence,  its  greatest  distance  must  be,  to  its  least  distance,  as 
59".  8  to  10,  or  nearly  as  6  to  1. 

The  learner  should  impress  this  fact  on  his  mind,  that  this 
planet  is  always  in  the  same  part  of  the  heavens  as  the  sun  — 
never  departing  more  than  47°  on  each  side  of  it — called  its 
greatest  elongation.  In  consequence  of  being  always  in.  the 
neighborhood  of  the  sun,  it  can  never  come  to  the  meridian 
near  midnight.  Indeed,  it  always  comes  to  the  meridian  within 
three  hours  twenty  minutes  of  the  sun,  and,  of  course,  in  day- 
light. But  this  does  not  prevent  meridian  observations  being 
taken  upon  it,  through  a  good  telescope  ;*  and,  as  to  this  par- 
ticular planet,  it  is  sometimes  so  bright  as  to  be  seen  by  the 
unassisted  eye  in  the  daytime. 

Even  without  instruments  and  meridian  observations,  the 
attentive  observer  can  determine  that  the  motion  of  Venus,  in 
relation  to  the  stars,  is  very  irregular  —  sometimes  its  motion 
is  very  rapid  —  sometimes  slow  —  sometimes  direct  —  some- 
times stationary,  and  sometimes  retrograde  ;\  but  the  direct 
motion  prevails,  and,  as  an  attendant  to  the  sun,  and  in  its  own 
irregular  manner,  as  just  described,  it  appears  to  traverse  round 
and  round  among  the  stars. 

But  Venus  is  not  the  only  planet  that  exhibits  the  appear- 
ances we  have  just  described.  There  is  one  other,  and  only 
one  —  Mercury;  a  very  small  planet,  rarely  visible  to  the  naked 

*  The  stars  continue  visible  through  telescopes,  during  the  day,  as  well 
as  the  night  ;  and  that,  in  proportion  to  the  power  of  the  instrument,  not 
only  the  largest  and  brightest  of  them,  but  even  those  of  inferior  luster, 
such  as  scarcely  strike  the  eye,  at  night,  as  at  all  conspicuous,  are  readily 
found  and  followed,  even  at  noonday,  by  those  who  possess  the  means  of 
pointing  a  telescope  accurately  to  the  proper  places  — unless  the  star  is  in 
that  point  of  the  heavens  very  near  the  sun. — HEKSCHEL. 

t  In  astronomy,  direct  motion  is  eastward  among  the  stars  ;  stationary  is 
no  apparent  motion  ;  and  retrograde  is  a  westward  motion. 

Is  the  distance  of  Venus  from  the  earth  very  variable,  and  how  great  is 
the  variation?  How  is  that  fact  ascertained  ?  Describe  the  apparent 
motion  of  Venus  among  the  stars.  What  is  understood  by  stationary, 
in  astronomy?  What  by  direct  and  retrograde  motions?  What  other 
planet  exhibits  like  appearances  to  Venus  1 


APPARENT  MOTIONS  OF  THE  PLANETS.  103 

eye,  and  not  known  to  the  very  ancient  astronomers.  "What- 
ever description  we  have  given  of  Venus  applies  to  Mercury, 
except  in  degree.  Its  variations  of  apparent  diameter  are  nob 
so  great,  and  it  never  departs  so  far  from  the  sun ;  and  the 
interval  of  time,  between  its  vibrations  from  one  side  to  the 
other  of  the  sun,  is  much  less  than  that  of  Venus. 

These  appearances  clearly  indicate  that  the  sun  must  be  the  center  t 
or  near  the  center,  of  these  motions,  and  not  the  earth;  and  tha 
Mercury  must  revolve  in  an  orbit  within  that  of  Venus. 

So  clear  and  so  unavoidable  were  these  inferences,  that  even 
the  ancients  (who  were  the  most  determined  advocates  for  the 
immobility  of  the  earth,  and  for  considering  it  as  the  principal 
object  in  creation  —  the  center  of  all  motion,  etc.)  were  com- 
pelled to  admit  them;  but  with  this  admission,  they  contended, 
that  the  sun  moved  round  the  earth,  carrying  these  planets  as 
attendants. 

By  taking  observations  on  the  other  planets,  the  ancient 
astronomers  found  them  variable  in  thei/  apparent  diameters, 
and  angular  motions ;  so  much  so,  that  ii  was  impossible  to  recon- 
cile appearances  viiih  the  idea  of  a  stationary  point  of  observation; 
unless  the  appearances  were  taken  for  realities,  and  that  was 
against  all  true  notions  of  philosophy. 

The  planet  Mars  is  most  remarkable  for  its  variations ;  and 
the  great  distinction  between  this  planet  and  Venus,  is,  that  it 
does  not  always  accompany  the  sun ;  but  it  sometimes,  yea,  at 
regular  periods,  is  in  the  opposite  pa?t  of  the  heavens  from  the 
sun — called  Opposition  —  at  which,  time  it  rises  about  sunset, 
and  comes  to  the  meridian  about  midnight. 

The  greatest  apparent  diameter  of  Mars  takes  place  when 
the  planet  is  in  opposition  to  the  sun,  and  it  is  then  17".l  ;  and 
its  least  apparent  diameter  takes  place  when  in  the  neigh bor- 

What  do  these  appearances  clearly  indicate  ?  "What  is  the  planet  Mars 
most  remarkable  for  ?  What  great  distinction  is  there  between  some  ap- 
pearances of  Mars  and  Venus  ?  When  a  planet  is  in  opposition  to  the  sun, 
•what  time  of  the  day  does  it  pass  the  meridian  ?  What  is  shown  by  the 
great  variation  in  the  apparent  diameter  of  Mars  ? 


104          ELEMENTARY  ASTRONOMY. 

hood  of  the  sun,  and  it  is  then  but  about  4";  showing  that  the 
sun,  and  not  the  earth,  is  the  center  of  its  motion. 

The  general  motion  of  all  the  planets,  in  respect  to  the  stars, 
is  direct;  that  is,  eastward;  but  all  the  planets  that  attain  op- 
position to  the  sun,  while  in  opposition,  and  for  some  time 
before  and  after  opposition,  have  a  retrograde  motion  —  and 
thoso  planets  which  show  the  greatest  change  in  apparent 
diameter,  show  also,  the  greatest  amount  of  retrograde  motion 
—  and  all  the  observed  irregularities  are  systematic  in  their 
irregularities,  showing  that  they  are  governed,  at  least,  by 
constant  and  invariable  laws.  If  the  earth  is  really  stationary, 
we  cannot  account  for  this  retrograde  motion  of  the  planets, 
unless  that  motion  is  real ;  and  if  real,  why,  and  how  can  it 
change  from  direct  to  stationary,  and  from  stationary  to  retro- 
grade, and  the  reverse? 

But  if  we  conceive  the  earth  in  motion,  and  going  the  same  ivay 
with  the  planet,  and  moving  more  rapidly  than  the  planet,  then  the 
planet  will  appear  to  run  back  /  that  is,  retrograde, 

And  as  this  retrogradation  takes  place  with  every  planet, 
when  the  earth  and  planet  are  both  on  the  same  side  of  the 
sun,  and  the  planet  in  opposition  to  the  sun  ;  and  as  these  cir- 
cumstances take  place  in  all  positions  from  the  sun,  it  is  a  suf- 
ficient explanation  of  these  appearances  ;  and  conversely,  then, 
these  appearances  show  the  motion  of  the  earth  in  an  orbit 
round  the  sun. 

When  a  planet  appears  to  be  stationary,  it  must  be  really  so, 
or  be  moving  directly  to  or  from  the  observer.  And  if  it  be 
moving  to  or  from  the  observer,  that  circumstance  will  be 
indicated  by  the  change  in  apparent  diameter;  and  observa- 
tions confirm  this,  and  show  that  no  planet  is  really  stationary, 
although  it  may  appear  to  be  so. 

If  we  suppose  the  earth  to  be  but  one  of  a  family  of  bodies, 
called  planets  —  all  circulating  round  the  sun  at  different 

When  do  planets  appear  to  retrograde  ?    When  a  planet  appears  to  be 
stationary,  is  it  really  so  ?    What  supposition  is  here  made  in  respect 
earth  ? 


APPARENT   MOTIONS  OF   THE  PLANETS.  105 

times  —  in  the  order  of  Mercury,  Venus,  Earth,  Mars,  (omitting 
the  small  telescopic  planets),  Jupiter,  Saturn,  Herschel,  or 
Uranus,  we  can  then  give  a  rational  and  simple  account  for 
every  appearance  observed,  and  without  discussing  the  ancient 
objections  to  the  true  theory  of  the  solar  system,  we  shall 
adopt  it  at  once,  and  thereby  save  time  and  labor,  and  intro- 
duce the  reader  into  simplicity  and  truth. 

This,  the  true  solar  system,  as  now  known  and  acknowledged, 
is  called  the  Copernican  system,  from  its  discoverer,  Coperni- 
cus, a  native  of  Prussia,  who  lived  some  time  in  the  fifteenth 
century. 

But  this  theory,  simple  and  rational  as  it  now  appears,  and 
capable  of  solving  every  difficulty,  was  not  immediately  adop- 
ted ;  for  men  had  always  regarded  the  earth  as  the  chief  object 
in  God's  creation  ;  and  consequently  man,  the  lord  of  creation, 
a  most  important  being.  But  when  the  earth  was  urled  from 
its  imaginary,  dignified  position,  to  a  more  humble  place,  it 
was  feared  that  the  dignity  and  vain  pride  of  man  must  fall 
with  it ;  and  it  is  probable  that  this  was  the  root  of  the  oppo- 
sition to  the  theory. 

So  violent  was  the  opposition  to  this  theory,  and  so  odious 
would  any  one  have  been  who  had  dared  to  adopt  it,  that  it 
appears  to  have  been  abandoned  for  more  than  one  hundred 
years,  and  was  revived  by  Galileo  about  the  year  1620,  who, 
to  avoid  persecution,  presented  his  views  under  the  garb  of  a 
dialogue  between  three  fictitious  persons,  and  the  points  left 
undecided.  But  the  caution  of  Galileo  was  not  sufficient,  or 
his  dialogue  was  too  convincing,  for  it  woke  up  the  Inquisition, 
and  he  was  forced  to  sign  a  paper  denouncing  tha  theory  as 
heresy,  on  the  pain  of  perpetual  imprisonment. 

Thus,  persecuting  error,  has  always  moved  in  advance  of 
truth,  and  though  powerful,  it  can  never  be  finally  successful. 

Who  discovered  the  true  solar  system  ?  Give  a  brief  outline  of  the  Co- 
pernican system  ?  Why  did  men  so  violently  oppose  this  system  ?  How 
long  was  this  system  lost,  and  how  can  we  account  for  its  being  neglected 
and  abandoned  ?  Who  revived  it  ?  What  trouble  did  thig  bring  ou  that 
Philosopher  ? 


10P 


ELEMENTARY  ASTRONOMY. 


CHAPTER   VI. 
THE    COPERNICAN    SYSTEM    ILLUSTRATED. 

THE  following  figure  is  designed  to  be  a  partial  representa- 
tion of  the  solar  system.  The  center  is  the  locality  of  the 
Sun,  and  the  innermost  circle  represents  the  orbit  of  Mercury, 
the  second  circle  the  orbit  of  Venus,  the  third  circle  the  orbit 
of  the  Earth,  and  the  outermost  circle  represents  the  orbit  of 
Mars. 


Whereabouts  in  the  solar  system  is  the  sun  located  ?     What  orbit  is 
nearest  to  the  sua  ?     What  orbit  docs  the  tkird  circle  represent  ? 


THE   COPERNICAX   SYSTEM   ILLUSTRATED.          107 

There  is  not  space  on  the  page  to  represent  the  orbit  of  tho 
planets,  beyond  or  more  remote  from  tjie  sun  than  Mars,  and, 
indeed,  there  is  not  space  to  represent  these  in  due  proportion, 
on  a  scale  of  sufficient  magnitude. 

Far,  far  away  beyond  the  orbits  of  the  planets  are  the  fixed 
stars  —  so  far,  that  the  whole  solar  system  is  but  a  point  in 
comparison.  To  help  the  imagination,  we  have  represented 
stars  about  the  borders  of  the  figure. 

Let  a,  b,  c,  d,  <fcc.  be  the  direct  course  of  the  planets  in  the 
heavens,  and  suppose  E  to  be  the  position  of  the  earth  at  some 
particular  time ;  then  we  know  that  those  stars,  a  little  in  ad- 
vance of  g,  will  come  to  the  meridian  at  midnight,  and  the  sun 
is  in  the  direction  of  the  stars,  near  b,  directly  opposite.  Let 
Jfbe  the  position  of  Mars,  and  Fthe  position  of  Venus.  The 
line  from  E  to  M,  extended  to  the  stars,  will  show  the  position 
of  Mars  among  the  stars  ;  and  a  line  from  E  to  V  shows  the 
position  of  Venus  among  the  stars  at  /.  Now  suppose  the 
earth  to  move  from  E  to  E ,,  and  during  the  same  time  Venus 
must  move  through  a  larger  arc,  as  from  Fto  F, ,  and  Mars 
move  through  a  lesser  arc,  as  from  M  to  M\ .  Now  Mars  appears 
to  have  gone  backward  among  the  stars,  and.  Venus  to  have 
moved  a  little  in  advance,  and  S  the  center  of  the  sun,  is  the 
only  point  in  the  solar  system  from  which  the  motion  of  the 
planets  can  appear  uniform  as  to  velocity  or  direction. 

When  the  earth  is  at  E\ ,  and  Mars  at  Mt ,  as  here  repre- 
sented the  apparent  diameter  of  Mars  is  greatest,  and  when 
Mars  is  in  its  orbit  beyond  the  sun,  its  apparent  diameter  is 
least,  as  was  noticed  in  the  preceding  chapter.  Indeed,  it  was 
appearances,  or  rather,  observations,  that  established  this 
theory  of  the  solar  system. 

Mercury  and  Venus,  never  coming  in  opposition  to  the  sun, 
but  revolving  around  that  body  in  orbits  that  are  within  that 
of  the  earth,  are  therefore  called  inferior  planets. 

Why  arc  Mercury  and  Venus  called  inferior  planets  ?  Why  are  all 
others  called  superior  planets  ?  To  the  inhabitants  of  Mars  is  the  Earth 
an  inferior  or  a  superior  planet  ? 


108 


ELEMENTARY  ASTRONOMY. 


Those  that  come  in  opposition,  and  thereby  show  that  their 
orbits  are  outside  of  the  earth,  are  called  superior  planets. 

We  shall  show  how  to  investigate  and  determine  the  position 
of  one  inferior  planet ;  and  the  same  principles  will  be  suffi- 
cient to  determine  the  position  of  any  inferior  planet. 

It  will  be  sufficient,  also,  to  investigate  and  determine  tho 
orbit  of  one  superior  planet ;  and,  if  that  is  understood,  it  may 
be  considered  as  substantially  determining  the  orbits  of  all  the 
superior  planets ;  and  after  that,  it  will  be  sufficient  to  state 
results. 

For  materials  to  operate  with,  we  give  the  following  table  of 
the  planetary  irregularities,  (so  called,)  drawn  from  obser- 
vation : 


PlanHs. 

Greater 
Apparent 
Diiimeters. 

Least 
Apparent 
Diameters. 

Angular  Distance 
from  gnn  at   the 
instant  of  Lem£ 
itntionaiv. 

Mean   arc  of 
Retrogradalion  . 

H 

// 

o      / 

0      / 

Mercury, 

11.3 

5.0 

18  00 

13  30 

Venus, 

59.6 

9.6 

28  48 

16  12 

Earth, 

Mars, 

17.1 

3.6 

136  48 

16  12 

Jupiter, 

44.5 

30.1 

115  12 

9  54 

Saturn, 

.     20.1 

16.3 

108  54 

6  18 

Uranus, 

41 

3.7 

103  30 

3  36 

On  the  supposition,  however,  that  the  planets  revolve  in 
circles  (which  is  not  for  from  the  truth),  the  greatest  and  least 
apparent  diameters  furnish  us  with  sufficient  data  to  compute 
the  distances  of  the  planets  from  the  sun  in  relation  to  the  dis- 
tance of  the  earth,  taken  as  unity. 

In  addition  to  the  facts  presented  in  the  preceding  table,  we 
must  not  fail  to  note  the  important  element  of  the  elongations 
of  Mercury  and  Venus.  This  term  can  be  applied  to  no  other 
planets. 

It  is  very  variable  in  regard  to  Mercury  —  showing  that  the 
orbit  of  that  planet  is  quite  elliptical.  The  variation  is  much 

"What  observations  will  furnish  means  to  determine  the  relative  distances 
of  the  planets  from  the  sun  ?  How  is  it  known  that  the  orbit  of  Mercury 
is  more  elliptical  than  that;  of  Yeiius  ? 


THE    COPERNICAN   SYSTEM   ILLUSTRATED.  109 

less  in  regard  to  Venus,  showing  that  Venus  moves  round  the 
sun  more  nearly  in  a  circle. 

For  Mercury.  For  Venus. 

The  least  extreme  elongation,          17°  37'  44°  58' 

The  greatest     "  "  28°     4'  47°  30' 

The  mean  elongation,  22°  46'  46°  20' 

Relying  on  these  facts  as  established  by  observations,  we 
can  easily  deduce  the  relative  orbits  of  Mercury  and  Venus. 

Let  S  represent  the  sun, 
E  the  earth,  V  Venus. 

Conceive  the  planet  to 
pass  round  the  sun  in  the 
direction  of  A  VB. 

The  earth  moves  also  in 
the  same  direction,  but 
not  so  rapidly  as  Venus. 

Now  it  is  evident  from 
inspection,  that  when  the 
planet  is  passing  by  the 
earth,  as  at  B,  it  will  ap- 
pear to  pass  along  in  the 
heavens  in  the  direction  of 
m  to  n.  But  when  the 
planet  is  passing  along  in 
its  orbit,  at  A,  and  the  earth  about  the  position  of  E,  the 
planet  will  appear  to  pass  in  the  direction  of  n  to  m.  When 
the  planet  is  at  V,  as  represented  in  the  figure,  its  absolute 
motion  is  nearly  toward  the  earth,  and,  of  course,  its  appear- 
ance is  nearly  stationary. 

It  is  absolutely  stationary  only  at  one  point,  and  even  then 
but  for  a  moment ;  and  that  point  is  where  its  apparent  motion 
changes  from  direct  to  retrograde,  and  from  retrograde  to  di- 

When  does  the  motion  of  the  inferior  planets  appear  most  direct  ?  When 
most  retrograde?  When  stationary?  Do  the  planets  appear  stationary 
for  any  considerable  time  ? 


110  ELEMENTARY  ASTRONOMY. 

rect ;  which  takes  place  when  the  angle  SEV  is  about  29 
degrees  on  each  side  of  the  line  SE. 

When  the  line  EV  touches  the    circumference  AVB,  the 
angle  SEV,  or  angle  of  elongation,  is  then  greatest;  and  the 
triangle  SEV  is  right  angled  at  V\  and  if  SE  is  made  radius, 
£  Twill  be  the  sine  of  the  angle  SEV. 

But  the  line  SE  is  assumed  equal  to  unity,  and  then  SV  will 
be  the  natural  sine  of  46°  20',  and  can  be  taken  out  of  any 
table  of  natural  sines  ;  or  it  can  be  computed  by  logarithms, 
and  the  result  is  .72336. 

For  the  planet  Mercury,  the  mean  of  the  same  angle  is  22° 
46,  and  the  natural  sine  of  that  angle,  or  the  mean  radius  of 
the  planet's  orbit,  is  .38698. 

Thus  we  have  found  the  relative  mean  distances  of  three 
planets  from  the  sun,  to  stand  as  follows : 

Mercury,         -  -  0.38698 

Venus,         -         -         -  -         -         -         0.72336 

Earth,     -  -  ...     1.00000 

If  the  orbits  were  perfect  circles,  then  the  angle  SEV  of 
greatest  elongation,  would  always  be  the  same  ;  but  it  is  an 
observed  fact  that  it  is  not  always  the  same  ;  therefore  the  orbits 
are  not  circles;  and  when  SVis  least,  and  SE  greatest,  then 
the  angle  of  elongation  is  least;  and  conversely,  when  /SF^is 
greatest  and  SE  least,  then  the  angle  of  elongation  is  the 
greatest  possible ;  and  by  observing  in  what  parts  of  the  heavens 
the  greatest  and  least  elongations  take  place,  we  can  approxi- 
mate to  the  positions  of  the  longer  axis  of  the  orbits. 

By  means  of  the  apparent  diameters,  we  can  also  find  the 
approximate  relations  of  their  orbits.  For  instance,  when  the 
planet  Venus  is  at  B,  and  appears  on  the  sun's  disc,  its  appa- 
rent diameter  is  59 '.6  ;  and  when  it  is  at  A,  or  as  near  A  as 
can  be  seen  by  a  telescope,  its  apparent  diameter  is  9". 6.  Now 
put 

SB=x;     then     EB=\—x;      and     AE=l+x. 

If  the  greatest  elongation  of  a,  planet  were  always  the  same,  what  would 
that  circumstance  show  ? 


THE    COPERmCAN    SYSTEM  ILLUSTRATED.  Ill 

By  Art.  66,          1—x  :  l+x  :  :  96  :  596  ; 

Hence,  #=0.72254. 

By  a  like  computation,  the  mean  distance  of  Mercury  from 
the  sun  is  0.3864. 

To  obtain  the  relative  distance  of  Mars  from  the  sun,  we 
proceed  as  follows  : 

Let  x  be  the  distance  sought ;  then  when  the  planet  is  nearest 
to  the  earth,  its  distance  must  be  expressed  by  (x — 1),  and 
when  at  its  greatest  distance  by  (x-\-\);  and  these  quantities 
must  be  to  each  other,  inversely, .as  the  observed  diameters; 
that  is,  we  have  the  following  proportion  ; 

x—  1     :     ar+1     :  :     3.6     :     17.1. 

Whence  #=1.53333. 

In  like  manner  we  may  obtain  the  relative  distance  of  any 
other  planet  from  the  sun. 

The  next  step  in  the  path  of  astronomical  knowledge  is  to 
determine  what  observations  are  necessary  to  find  the  periodical 
revolutions  of  the  planets  around  the  sun.  If  observers  on 
the  earth  were  at  the  center  of  motion,  they  could  determine 
the  times  of  revolution  by  simple  observation.  But  as  the 
aarth  is  one  of  the  planets,  and  all  observers  on  its  surface  are 
carried  with  it,  the  observations  here  made  must  be  subjected 
to  mathematical  corrections,  to  obtain  true  results  ;  and  this 
was  an  impossible  problem  to  the  ancients,  as  long  as  they 
contended  for  a  stationary  earth. 

If  the  observer  could  view  the  planets  from  the  center  of 
the  sun,  he  would  see  them  in  their  true  places  among  the 
stars  —  and  there  are  only  two  positions  in  which  an  observer 
on  the  earth  will  see  a  planet  in  the  same  place  as  though  he 
viewed  it  from  the  center  of  the  sun,  and  these  positions  are 
conjunction  and  opposition. 

By  what  means  can  astronomers  obtain  the  relative  distances  of  the 
superior  planets  from  the  sun  ?  What  is  the  next  step  in  astronomical 
knowledge?  Why  cannot  the  periodical  revolutions  of  the  planets  be 
observed  directly? 


H2          ELEMENTARY  ASTRONOMY. 

Thus,  when  the  earth  is  at  JZ,  and  the  planet  at  M,  the 
planet  is  in  opposition  to  the  sun  ;  and  it  is  seen  projected 
among  the  stars  at  the  same  point,  whether  viewed  from  S  or 
from  E. 

The  time  that  any  planet  comes  in  opposition  to  the  sun,  can 
be  very  distinctly  determined  by  observation.  Its  longitude 
is  then  180  degrees  from  the  longitude  of  the  sun,  and  comes 
to  the  meridian  nearly  or  exactly  at  midnight.  If  it  is  a  little 
short  of  opposition  at  the  time  of  one  observation,  and  a  little 
past  at  another,  the  observer  can  proportion  to  the  exact  time 
of  opposition,  and  such  timer  can  be  definitely  recorded  —  and 
by  such  observation,  we  have  the  true  position  of  the  planet, 
as  seen  from  the  sun. 

Now  suppose  the  planet 
at  E  to  pass  on  and  make 
a  revolution,  and  when  it 
comes  round  to  E  again, 
the  planet  M  is  near  m, 
and  the  planet  at  E  has  to 
pass  on  to  E\  before  the 
planet  is  again  in  opposi- 
tion to  the  sun. 

During  this  time,  the 
earth,  or  inferior  planet,  must 
describe  one  revolution,  and 
the  arc  MSm,  and  the  supe- 
rior planet  must  describe 
the  excess  arc  MSm. 

The  time  from  one  of 
these  oppositions  of  the  same  planet  to  another,  is  called  the 
synodic  revolution  of  the  planet,  and  observations  have  furnished 
us  with  the  facts  as  stated  in  the  following  table  : 

When  can  we  nee  a  planet  in  the  same  position  among  the  stars  as  though 
it  were  seen  from  the  center  of  the  sun?  What  is  understood  by  the  synod- 
ical  revolution  wf  a  planeL  ? 


THE   COPERNICAN    SYSTEM   ILLUSTRATED. 


113 


Planets. 

Mean  Durai  ion  of 
the  Retrograde 
motion. 

Mean  Duration  of  the  Synodic 
Revolution,  or  interval  between 
two  successive  oppositions. 

Mercury, 
Venus, 
Earth, 
Mars, 
Jupiter, 
Sauirn, 
Uranus, 

23  days. 
42     " 

75     " 

121      " 
139     " 
151     " 

1  1  8  days. 

584      " 

780     « 

378     " 
370     " 

In  the  preceding  table,  the  word  mean  is  used  at  the  head  of 
the  several  columns,  because  these  elements  are  variable — some- 
times more,  and  sometimes  less,  than  the  numbers  here  given 
—  which  indicate  that  the  planets  •  do  not  revolve  in  circles 
round  the  sun,  but  most  probably  in  ellipses,  like  the  orbit  of 
the  earth. 

Let  us  now  take  the  time  of  the  synodic  revolution  of  Jupi- 
ter, from  the  above  table,  and  from  it  determine  the  periodical 
revolution  of  that  planet.  In  365.256  days  the  earth  describes 
a  revolution,  or  360°,  at  an  average  rate  of  59'  8"  per  day. 
From  399  days  subtract  365.256  days,  and  the  difference  ia 
33.744  days.  In  33.744  days  at  59'  8"  per  day,  the  earth  will 
describe  33°. 256,  which  is  the  arc  that  Jupiter  describes  in 
399  days,  as  seen  from  the  sun.  How  many  days  then  will  be 
required  by  that  planet  to  describe  360°?  The  proportion 
stands  thus  : 

33°.256  :  360°  :  :  299  :  the  time  required. 

This  proportion  gives  a  little  over  4319  days  for  the  sidereal 
revolution  of  Jupiter.  The  true  time  is  a  little  over  4332  days, 
the  cause  of  the  difference  will  soon  be  explained. 

Let  us  now  determine,  approximately,  the  sidereal  evolution 
of  Venus. 

Its  synodic  revolution  is  put  down  at  584  days.  In  this  time 
the  earth  describes  (575.58)  degrees,  but  because  Venus  is  an 
inferior  planet,  it  describes  one  revolution  more.  Therefore  Venus 

Why  do  astronomers  use  the  word  mean,  so  often?  In  a  synodic  revo- 
lution, how  many  degrees  does  one  planet  describe  more  than  the  other? 
Which  one  describes  the  greatest  number  of  degrees? 

to 


114          ELEMENTARY  ASTRONOMY. 

must  describe  935.58  degrees  in  584  days.     In  what  time  then 
will  that  planet  describe  360  degrees? 
The  proportion  is  this  : 

935  jW  :  360  :  :  584  :  the  time  sought. 

The  result  of  this  proportion  gives  224^  days  for  the  side- 
real revolution  of  Venus,  which  is  very  near  the  truth. 

All  these  results  are,  of  course,  understood  as  first  approxi- 
mations, and  accuracy  here  is  not  attempted.  We  are  only 
showing  principles  ;  and  it  will  be  noticed,  that  the  times  here 
taken  in  these  computations,  are  only  to  the  nearest  days,  and 
not  fractions  of  a  day,  as  would  be  necessary  for  accurate 
results.  By  this  method,  accuracy  is  never  attained,  on 
account  of  the  eccentricities  of  the  orbits.  No  two  synodical 
revolutions  are  exactly  alike  ;  and  therefore  it  is  very  difficult 
to  decide  what  the  real  mean  values  are. 

To  obtain  accuracy,  in  astronomy,  observations  must  be 
carried  through  a  long  series  of  years.  The  following  is  an 
example  :  and  it  will  explain  how  accuracy  can  be  attained  in 
relation  to  any  other  planet. 

On  the  7th  of  November,  1631,  M.  Cassini  observed  Mercury 
passing  over  the  sun  ;*  and  from  his  observations  then  taken, 
deduced  the  time  of  conjunction  to  be  at  7h.  50m.,  mean  time, 
at  Paris,  and  the  true  longitude  of  Mercury  44°  41'  35". 

Comparing  this  occultation  with  that  which  took  place  in 
1723,  the  true  time  of  conjunction  was  November  9th,  at  5h. 
29m.  p.  M.,  and  Mercury's  longitude  was  46°  47'  20". 

The  elapsed  time  was  92  years,  2  days,  9  hours,  39  minutes. 

*  The  times  when  Mercury  and  Venus  are  seen  in  the  same  part  of  the 
heavens  from  the  sun  as  from  the  earth,  can  only  he  observed  from  the  earth 
when  these  planets  are  in  a  line  between  the  earth  and  some  part  of  the 
sun.  The  planet  will  then  appear  on  the  sun  as  a  black  spot,and  then  it  is 
called  an  occultation. 

Why  is  accuracy  as  to  the  times  of  revolution  of  the  planets  never  at- 
tempted to  be  deduced  from  a  synodic  revolution?  How  then  is  accuracy 
attained  ?  Why  did  the  author  introduce  a  method  that  could  not  be  relied 
u/  HI  for  accuracy  ? 


THE  COPERNICAN   SYSTEM   ILLUSTRATED.  115 

Twenty-two  of  these  years  were  bissextile  ;  therefore  the 
elapsed  time  was  (92X365)  days,  plus  24d.  9h.  39m. 

la  this  interval,  Mercury  made  382  revolutions,  and  2°  5' 
45"  over.  That  is,  in  33604.402  days,  Mercury  described 
137522.095826  degrees  ;  and  therefore,  by  division,  we  find 
that  in  one  day  it  would  describe  4°. 0923,  at  a  mean  rate. 

Thus,  knowing  the  mean  daily  rate  to  great  accuracy,  the 
mean  revolution,  in  time,  must  be  expressed  by  the  fraction 

Qflfl 

.  oou    =87.9701  days,  or  87  days  23  h.  15m.  57s. 
4.0923 

The  following  is  another  method  of  observing  the  periodical 
times  of  the  planets,  to  which  we  call  the  student's  special  attention. 

The  orbits  of  all  the  planets  are  a  little  inclined  to  the  plane 
of  the  ecliptic. 

The  planes  of  all  the  planetary  orbits  pass  through  the  center 
of  the  sun ;  the  plane  of  the  ecliptic  is  one  of  them,  and  there- 
fore the  plane  of  the  ecliptic  and  the  plane  of  any  other  planet 
must  intersect  each  other  by  some  line  passing  through  the 
center  of  the  sun.  The  intersection  of  two  planes  is  always  a 
straight  line.  (See  Geometry.) 

The  reader  must  also  recognize  and  acknowledge  the  follow- 
ing principle  : 

That  a  body  cannot  appear  to  be  in  the  plane  of  an  observer,  un- 
less it  really  is  in  that  plane. 

For  example  :  an  observer  is  always  in  the  plane  of  his 
meridian,  and  no  body  can  appear  to  be  in  that  plane  unless  it 
really  is  in  that  plane ;  it  cannot  be  projected  in  or  out  of  that 
plane,  by  parallax  or  refraction. 

Hence,  when  any  one  of  the  planets  appears  to  be  in  the 
plane  of  the  ecliptic,  it  actually  is  in  that  plane  ;  and  let  the 
time  be  recorded  when  such  a  thing  takes  place. 

The  planet  will  immediately  pass  out  of  the  plane,  because 
the  two  planes  do  not  coincide.  Passing  the  plane  of  the 

Do  the  planets  appear  to  pass  along  in  the  heavens  in  the  plane  of  the 
ecliptic  ?  Can  a  planet  appear  to  be  in  the  ecliptic  unless  it  is  really  in 
tfiat  place  ? 


1 1 6  ELEMENTARY  ASTRONOMY. 

ecliptic  is  called  passing  the  node.  Keep  track  of  the  planet 
until  it  comes  into  the  same  plane  ;  that  is,  crosses  the  other 
node :  in  this  interval  of  time  the  planet  has  described  just 
180°,  as  seen  from  the  sun  (unless  the  nodes  themselves  are  in 
motion,  which  in  fact  they  are  ;  but  such  motion  is  not  sensible 
for  one  or  two  revolutions  of  Venus  or  Mars.) 

Continue  observations  on  the  same  planet,  until  it  comes  into 
the  ecliptic  the  second  time  after  the  first  observation,  or  to 
the  same  node  again ;  and  the  time  elapsed,  is  the  time  of  a  revo- 
lution of  that  planet  round  the  sun.  From  such  observations  the 
periodical  time  of  Venus  became  well  known  to  astronomers, 
long  before  they  had  opportunities  to  decide  it  by  comparing 
its  transits  across  the  sun's  disc ;  and  by  thus  knowing  its 
periodical  time  and  motion,  they  were  enabled  to  calculate  the 
times  and  circumstances  of  the  transits  which  happened  ill 
1761,  and  in  1769 ;  save  those  resulting  from  parallax  alone. 

From  observations  long  continued  and  accurately  made,  the 
following  results  were  long  since  established : 

Sidereal  Revolutions.  Mean  distances  from  Q 

Mercury,     -     -     87.969258  0.387098 

Venus,     -     -       224.70Q787  0.723332 

Earth,    -     -     -  365.256383  1.000000 

Mars,       -"    -       686.979646  1.523692 

Jupiter,     -     -  4332.584821  5.202776 

Saturn,   -     -   10759.219817  9.538786 

Uranus,      -      3C686. 820830  19.182390 

By  inspecting  this  table,  we  shall  perceive  that  the  greater 
the  distance  from  the  sun  the  greater  the  time  of  revolution, 
but  the  increase  of  the  times  of  revolution  is  much  greater 
than  the  increase  of  distances.  This  shows  that  the  greater 
the  distance  a  planet  is  from  the  sun,  the  slower  is  its  actual 
motion.* 

*  Let  the  reader  be  careful  not  to  confound  real  or  actual  motion  with 
anyular  motion. 

B}T  what  observation  can  the  periodical  revolution  of  a  planet  be  observed 
directly  ?  Do  the  times  of  revolution,  and  the  distances  from  the  sun,  in- 
crease in  the  same  ratio  ? 


THE    COPERNICAN   SYSTEM   ILLUSTRATED.  117 

Kepler,  a  Danish  philosopher,  about  the  year  1617,  after 
various  comparisons  of  the  increase  of  time  with  the  increase 
of  distance,  found  that  the  square  of  the  revolution  corres- 
ponded to  the  cube  of  the  distance,  and  thus  established  his 
third  law. 

We  may  now  recapitulate  the  three  law  of  the  solar  system, 
called  Kepler's  laws. 

1st.  The  orbits  of  the  planets  are  ellipses,  of  which  the  sun 
occupies  one  of  the  foci. 

2d.  The  radius  vector  in  each  case  describes  areas  about  the 
focus,  which  are  proportional  to  the  times. 

3d.  The  squares  of  the  times  of  revolution  are  to  each  other  as 
the  cubes  of  the  mean  distances  from  the  sun. 

The  first  of  these  laws  is  nothing  more  than  an  observed 
fact :  —  the  second  and  third  are  also  observed  facts,  and  are 
susceptible  of  mathematical  demonstration  on  philosophical 
principles,  as  may  be  seen  in  our  University  Edition  of  As- 
tronomy, and  in  our  Mathematical  Sequel. 

Kepler's  third  law  is  of  great  practical  utility  in  finding  the 
mean  distances  of  any  newly  discovered  planets  from  the  sun. 

Thus,  suppose  a  new  planet  should  be  discovered,  whose 
time  of  revolution  round  the  sun  was  just  five  years,  what 
would  be  its  mean  distance  from  the  sun  ? 

Let  x  represent  the  distance  sought. 

Then  I2     :     52     :  :     I3     :    z3. 

Whence  #3=25,         or         #=2.924. 

That  is,  the  distance  of  that  planet  from  the  sun  must  be 
2.924  times  the  distance  between  the  sun  and  the  earth. 

Repeat  Kepler's  laws.  Make  a  proportion  with  the  numbers  taken  from 
the  table,  to  show  that  you  understand  the  enunciation  of  the  third  law. 


1 1 8  ELEMENTARY  ASTRONOMY. 


CHAPTER  VII. 

THE   TRANSITS    OF  VENUS  AND  MERCURY  — THE  SUN'S 

HORIZONTAL  PARALLAX  — THE  REAL  MAGNITUDE 

AND  DISTANCE  TO  THE  SUN. 

WE  have  thus  far  been  very  patient  in  our  investigations  — « 
groping  along  —  finding  the  form  of  the  planetary  orbits,  and 
their  relative  magnitudes ;  but,  as  yet,  we  know  nothing  of  the 
distance  to  the  sun,  save  the  indefinite  fact,  that  it  must  be 
very  great,  and  its  magnitude  great ;  but  how  great,  we  can 
never  know,  without  the  sun's  parallax.  Hence,  to  obtain 
this  element,  has  always  been  an  interesting  problem  to  as- 
tronomers. 

The  ancient  astronomers  had  no  instruments  sufficiently 
refined  to  determine  this  parallax  by  direct  observation,  in  the 
manner  of  finding  that  of  the  moon,  and  hence  the  ingenuity 
of  men  was  called  into  exercise  to  find  some  artifice  to  obtain 
the  desired  result. 

After  Kepler's  laws  were  established,  and  the  relative  dis- 
tances of  the  planets  made  known,  it  was  apparent  that  their 
real  distance  could  be  deduced,  provided,  the  distance  between 
the  earth  and  any  planet  could  be  made  known. 

The  relative  distances  of  the  earth  and  Mars,  from  the  sun 
(as  determined  by  Kepler's  law)  are  as  1  to  1.5237  ;  and  hence 
it  follows  that  Mars,  in  its  oppositions  to  the  sun,  is  but  about 
one  half  as  far  from  the  earth  as  the  sun  is;  and  therefore  its 
parallax  must  be  about  double  that  of  the  sun ;  and  several 
partially  successful  attempts  were  made  to  obtain  it  by  obser- 
vations. 

On  the  15th  of  August,  1719,  Mars  being  very  near  its 
opposition  to  the  sun,  and  very  near  a  star  of  the  5th  magni- 
tude, its  parallax  became  sensible  ;  and  Mr.  Maraldi,  an  Italian 

When  Mars  is  in  opposition  to  the  sun,  how  much  greater  is  its  parallax 
than  the  parallax  of  the  sun? 


SOLAR   PARALLAX.  119 

astronomer,  pronounced  it  to  be  27".  The  relative  distance  of 
Mars,  at  that  time,  was  1.37,  as  determined  from  its  position 
and  the  eccentricity  of  its  orbit. 

But  horizontal  parallax  is  the  angle  under  which  the  semi- 
diameter  of  the  earth  appears  ;  and,  at  a  greater  distance,  it  will 
appear  under  a  less  angle.  The  distance  of  Mars  from  the 
earth,  at  that  time,  was  .37,  and  the  distance  of  the  sun  was  1; 

Therefore,    1     :     .37     :   :     27"     :     9".99,  or  10"  nearly, 
for  the  sun's  horizontal  parallax. 

On  the  6th  of  October,  1751,  Mars  was  attentively  observed 
by  Wargentin  and  Lacaille  (it  being  near  its  opposition  to  the 
sun),  and  they  found  its  parallax  to  be  24". 6,  from  which  they 
deduced  the  mean  parallax  of  the  sun,  10".7.  But  at  that  time, 
if  not  at  present,  the  parallax  of  Mars  could  not  be  observed 
directly,  with  sufficient  accuracy  to  satisfy  astronomers  ;  for  no 
observer  could  rely  on  an  angular  measure  within  2". 

Not  being  satisfied  with  these  results,  Dr.  Halley,  an  English 
astronomer,  very  happily  conceived  the  idea  of  finding  the  sun's 
parallax  by  the  comparisons  of  observations  made  from  different 
parts  of  the  earth,  on  a  transit  of  Venus  over  the  sun's  disc. 
If  the  plane  of  the  orbit  of  Venus  coincided  with  the  orbit  of 
the  earth,  then  Venus  would  come  between  the  earth  and  sun 
at  every  inferior  conjunction,  at  intervals  of  584.04  days.  But 
the  orbit  of  Venus  is  inclined  to  the  orbit  of  the  earth  by  an 
angle  of  3°  23'  28";  and,  in  the  year  1800,  the  planet  crossed 
the  ecliptic  from  south  to  north,  in  longitude  74°  54'  12",  and 
from  north  to  south,  in  longitude  254°  54'  12":  the  first  men- 
tioned point  is  called  the  ascending  node;  the  last,  the  descending 
node.  The  nodes  retrograde  31'  10"  in  a  century. 

The  mean  synodical  revolution  of  584  days  corresponds  with 
no  aliquot  part  of  a  year;  and  therefore,  in  the  course  of  time, 
these  conjunctions  will  happen  at  different  points  along  the 
ecliptic.  The  sun  is  in  that  part,  of  the  ecliptic  near  the  nodes 

Who  conceived  the  idea  of  deducing  the  sun's  parallax  from  a  transit  of 
Venus?  Why  is  there  not  a  transit  at  every  inferior  conjunction  of  Venua 
with  the  sun  ? 


120          ELEMENTARY  ASTRONOMY. 

of  Venus,  June  5th  and  December  6th  or  7th ;  and  the  two  last 
transits  happened  in  1761  and  1769  ;  and  from  these  periods  we 
date  our  knowledge  of  the  solar  parallax. 

The  periodical  revolution  of  the  earth  is  365.256383  days, 
and  that  of  Venus  is  224.700787  days  ;  and  as  numbers  they 
are  nearly  in  proportion  of  13  to  8;  more  nearly  as  382  to  235. 

From  this  it  follows,  that  eight  revolutions  of  the  earth  re- 
quire nearly  the  same  time  as  thirteen  revolutions  of  Venus ; 
and,  of  course,  whenever  a  conjunction  takes  place,  eight  years 
afterward,  another  conjunction  will  take  place  very  near  the 
same  point  in  the  ecliptic. 

If  the  proportional  revolutions  were  exactly  as  13  to  8,  then 
the  conjunctions  at  these  periods  would  always  take  place 
exactly  in  the  same  point  in  the  heavens ;  but  as  it  is,  conjunc- 
tions take  place  east  and  west  of  that  point,  and  approximate 
nearer  to  it  in  periods  more  nearly  proportional  to  the  revolu- 
tion of  the  planets. 

To  be  more  practical,  however,  the  intervals  between  con- 
junctions are  such,  combined  with  a  slight  motion  of  the  nodes, 
that  the  geocentric  latitude  of  Venus,  at  inferior  conjunctions 
near  the  ascending  node,  changes  about  19'  30"  to  the  north, 
in  a  period  of  about  eight  years.  At  the  descending  node,  it 
changes  about  the  same  quantity  to  the  southward,  in  the  same 
period ;  and  as  the  disc  of  the  sun  is  but  little  over  32',  it  is 
impossible  that  a  third  transit  should  happen  sixteen  years  after 
the  first;  hence,  only  two  transits  can  happen,  at  the  same 
node,  separated  by  the  short  interval  of  eight  years. 

If  at  any  transit  we  suppose  Venus  to  pass  directly  over  the 
center  of  the  sun,  as  seen  from  the  center  of  the  earth  —  that 
is,  pass  conjunction  and  node  at  the  same  time  —  at  the  end  of 
another  period  of  about  eight  years,  Venus  would  be  19'  30" 
north  or  south  of  the  sun's  center ;  but  as  the  semi-diameter 
of  the  sun  is  but  about  16',  no  transit  could  happen  in  such  a 

If  Venus  should  pass  over  the  center  of  the  sun  at  any  inferior  conjunc- 
tion, should  we  have  another  transit  in  eight  years  after?  How  far  would 
Venus  then  pass  from  the  limb  of  the  S'ui  ? 


SOLAR   PARALLAX.  121 

case ;  and   there  would  be  but  one  transit  at  that  node  until 
after  the  expiration  of  a  long  period  of  235  or  243  years. 

After  passing  the  period  of  eight  years,  we  take  a  lapse  of 
105  or  113  years,  or  thereabouts,  to  look  for  a  transit  at  the 
other  node. 

Knowing  the  relative  distances  of  Venus,  and  the  earth,  from 
the  sun  —  the  positions  and  eccentricities  of  both  orbits  —  also 
their  angular  motions  and  periodical  revolutions  —  every  cir- 
cumstance attending  a  transit,  as  seen  from  the  earth's  center, 
can  be  calculated;  and  Dr.  Halley,  in  1677,  read  a  paper  be- 
fore the  London  Astronomical  Society,  in  which  he  explained 
the  manner  of  deducing  the  parallax  of  the  sun  from  observa- 
tions taken  on  a  transit  of  Venus  or  Mercury  across  the  sun's 
disc,  compared  with  computations  made  for  the  earth's  center, 
or  by  comparing  observations  made  on  the  earth  at  great  dis- 
tances from  each  other. 

The  transits  of  Venus  are  much  better,  for  this  purpose, 
than  those  of  Mercury  ;  as  Venus  is  larger,  and  nearer  the 
earth,  and  its  parallax  at  such  times  much  greater  than  that  of 
Mercury  ;  and  so  important  did  it  appear,  to  the  learned  world, 
to  have  correct  observations  on  the  last  transit  of  Venus,  in 
1769,  at  remote  stations,  that  the  British,  French,  and  Russian 
governments  were  induced  to  send  out  expeditions  to  various 
parts  of  the  globe,  to  observe  it.  "  The  famous  expedition  of 
Captain  Cook,  to  Otaheite,  was  one  of  them." 

The  mean  result  of  all  the  observations  made  on  that  mem- 
orable occasion,  gave  the  sun's  parallax,  on  the  day' of  the 
transit,  (3d  of  June,)  8". 5776.  The  horizontal  parallax,  at 
mean  distance,  may  be  taken  at  8".6 ;  which  places  the  sun,  at 
its  mean  distance,  no  less  than  23984  times  the  length  of  the 
earth's  semi-diameter,  or  about  95  millions  of  miles. 

This  problem  of  the  sun's  horizontal  parallax,  as  deduced 
from  observations  on  a  transit  of  Venus,  we  regard  as  the  most 

Why  are  transits  of  Venus  better  for  this  object  than  those  of  Mercury? 
What  is  the  amount  of  the  sun's  parallax  ?    What  is  then  the  distance  to 
the  sun,  in  miles  ? 
11 


122          ELEMENTARY  ASTRONOMY. 

important,  for  a  student  to  understand,  of  any  in  astronomy  ; 
for  without  it,  the  dimensions  of  the  solar  system,  and  the 
magnitudes  of  the  heavenly  bodies,  must  be  taken  wholly  on 
trust ;  and  we  have  often  protested  against  mere  facts  being 
taken  for  knowledge. 

We  shall  now  attempt  to  explain  this  whole  matter  on  gen- 
eral principles,  avoiding  all  the  little  minutiae  which  render  the 
subject  intricate  and  tedious  ;  for  our 
only  object  is  to  give  a  clear  idea 
of  the  nature  and  philosophy  of  the 
problem. 

Let  S  represent  the  sun,  and  m  n  and 
PQ  small  portions  of  the  orbits  of 
Venus,  and  the  earth. 

As  these  two  bodies  move  the  same 
way,  and  nearly  in  the  same  plane,  we 
may  suppose  the  earth  stationary,  and 
Venus  to  move  with  an  angular  velocity 
equal  to  the  difference  of  the  two. 

When  the  planet  arrives  at  v,  an  ob- 
server at  G  would  see  the  planet  pro- 
jected on  the  sun,  making  a  dent  at  v'. 
But  an  observer  at  A  would  not  see 
the  same  thing  until  after  the  planet 
had  passed  over  the  small  arc  vq,  with 
a  velocity  equal  to  the  difference  be- 
tween the  angular  motion  of  the  two 
bodies  ;  and  as  this  will  require  quite 
an  interval  of  absolute  time,  it  can  be 
detected;  and  it   measures  the  angle 
an  angle  under  which  a  definite  portion  of  the  earth 
appears  as  seen  from  the  sun. 

To  have  a  more  definite  idea  of  the  practicability  of  this 

If  two  observers  are  at  a  distance  from  each  other,  will  they  see  the  be- 
ginning or  end  of  the  transit  at  the  same  time  ?  Is  it  the  object  of  tlia 
observations  to  determine  the  difference  in  the  time  ? 


SOLAR  PARALLAX.  123 

method,  let  us  suppose  the  parallactic  angle,  Av'Gf,  equal  to 
10",  and  inquire  how  long  Venus  would  be  in  passing  the  rela- 
tive arc  vq. 

Venus,  at  its  mean  rate,  passes     -       1°  36'  8"  in  a  day. 

The  earth,         "         "         "     -     -          59'  8" 

The  relative,  or  excess  motion  of  Venus  for  a  mean  solar 
day,  is  then  37'. 

Now  as  37'  is  to  24h.  so  is  10"  to  a  fourth  term  ;  or  as 
2220"     :     1440m.     :   :     10"     :     6m.  29s. 

Now  if  observation  had  given  more  than  6  minutes  and  29 
seconds,  we  should  conclude  that  the  parallactic  angle  was 
more  than  10";  if  less,  less.  But  this  is  an  abstract  proposition. 
When  treating  of  an  actual  case  in  place  of  the  mean  motion, 
we  must  take  the  actual  angular  motions  of  the  earth  and  Venus 
at  that  time,  and  we  must  know  the  actual  position  of  the  ob- 
servers A  and  G  in  respect  to  each  other,  and  the  position  of 
each  in  relation  to  a  line  joining  the  center  of  the  sun ;  and 
then  by  comparing  the  local  time  of  observation  made  at  A, 
•with  the  time  at  G,  and  referring  both  to  one  and  the  same 
meridian,  we  shall  have  the  interval  of  time  occupied  by  the 
planet  in  passing  from  v  to  q,  from  which  we  deduce  the  paral- 
lactic angle  Av'G,  and  from  thence  the  horizontal  parallax,  or 
the  magnitude  that  the  angle  A  v  Q-  would  be,  in  case  the  dis- 
tance AC?  were  equal  to  the  semi-diameter  of  the  earth. 

The  same  observations  can  be  made  when  the  planet  passes 
off  the  sun,  and  a  great  many  stations  can  be  compared  with 
A,  as  well  as  the  station  G.  In  this  way,  the  mean  result  of 
a  great  many  stations  was  found  in  1761,  and  in  1769,  and  the 
mean  of  all  cannot  materially  differ  from  the  truth. 

The  first  transit  known  to  have  been  observed  was  in  1639, 
December  4th;  to  this  add  225  years,  and  we  have  the  time  of 
the  next  transit,  at  the  same  node,  1874,  December  8th;  and 
eight  years  after  that  will  be  another,  1882,  December  6th. 

Has  the  parallax  of  the  sun  been  deduced  from  one  observation,  or  is  it 
the  result  of  many?  Can  this  result  be  far  from  the  truth?  When  \vill 
the  next  transit  occur? 


124  ELEMENTARY  ASTRONOMY. 


CHAPTER    VIII. 

TO    FIND    THE    DIAMETER    AND   MAGNITUDE   OF 
A    PLANET. 

HAVING  now  found  the  solar  horizontal  parallax,  and  conse- 
quently the  real  distance  to  the  sun,  we  have  sufficient  data  to 
find  the  real  distance,  diameter,  and  magnitude  of  each  and 
every  planet  in  the  solar  system. 

Let  the  reader  bear  in  mind  that  the  horizontal  parallax  of 
any  body  is  the  angle  under  which  the  semi-diameter  of  the 
earth  appears,  as  seen  from  that  body.     The  apparent  semi- 
diameter  of  the  body,  and  the  earth's  horizontal  parallax,  as 
seen  from  that  body,  is  one  and  the  same  thing ;  therefore, 
As  the  diameter  of  the  earth 
Is  to  the  diameter  of  any  other  planet, 
So  is  the  horizontal  parallax  of  the  planet 
To  its  apparent  semi-diameter. 

The  mean  horizontal  parallax  of  the  sun,  as  determined  by 
the  transit  of  Venus,  is  8".6,  and  the  semi-diameter  of  the  sun 
at  the  corresponding  mean  distance,  is  16'  1",  or  961".  Now 
let  d  represent  the  real  diameter  of  the  earth,  and  D  that  of 
the  sun,  then  we  shall  have  the  following  proportion  : 

d     :     D     :  :     8".6     :,   961".0 

But  d  is  7912  miles  ;  and  the  ratio  of  the   last  two  terms  is 
111.66;  therefore  JZ>=(111.66)(7912)  =  883454  miles. 

The  sun's  horizontal  parallax  is  the  angle  at  the  vertex  of 
a  right  angled  triangle,  and  the  base  opposite,  is  the  semi- 
diameter  of  the  earth  ;  and  if  we  call  that  distance  unity,  and 
compute  the  distance  of  one  of  the  other  sides  by  trigonometry, 
we  shall  find  it  equal  to  23984  units,  or  semi-diameters  of  the 

What  element  must  astronomers  obtain  before  they  can  determine  the 
magnitudes  and  distances  of  the  planets?  State  the  rule  to  find  the  diam- 
eter of  the  suu  or  a  planet  ? 


DIAMETERS  AND  MAGNITUDES  OF  THE  PLANETS.    125 


earth  ;  but  to  aid  the  memory,  we  may  say  that  the  distance  is 
24000  times  the  earth's  semi-diameter. 

If  we  change  the  unit,  from  the  semi-diameter  of  the  earth,  to 
an  English  mile,  then  the  mean  distance  between  the  earth  and 
sun  must  be 

(3956)(24000)=94.944000  miles. 
In  round  numbers  we  may  say  95  millions  of  miles. 
By  Kepler's  third  law,  we  know  the  relative  distances  of 
the  planets  from  the  sun,  and  now  knowing  the  real  distance, 
in  miles,  of  one  of  them  (the  earth),  we  can  determine  the  real 
distances  of  the  others  by  multiplying  each  relative  distance 
by  94.944000. 

Relative  distances.  True  distances. 

36.752.822 
68.672.995 

94.944000=         94.944.000 
144.666.172 
493.974.643 
905.651.827 
L  1814.417.800  ' 
By  observations  taken  on  the  transit  of  Venus,  in  1769,  it, 
was  concluded  that  the  horizontal  parallax  of  that  planet  was 
30".4 ;  and   its  semi-diameter,  at  the  same  time,  was  29".2. 
Hence,  304  :  292  :  :  7912  :  to  a  fourth  term;    which  gives 
7599  miles  for  the  diameter  of  Venus. 

.  We  cannot  observe  the  horizontal  parallax  of  Jupiter,  Saturn, 
or  any  other  very  remote  planet :  if  known  at  all,  it  becomes 
known  by  computation ;  but  the  parallax  of  the  sun  being  now 
known,  and  the  relative  distances  of  the  earth  and  all  the 
planets  from  the  sun  being  known,  the  horizontal  parallax  of 
any  planet  can  be  computed  as  follows.  Once  more  we  remind 
the  reader  that  the  sun's  horizontal  parallax  is  the  angle  under 
which  the  earth  appears,  as  seen  from  the  sun — seen  from  a 

What  is  the  multiplier  to  the  relative  distances  of  the  planets  from  the 
sun,  to  obtain  the  distances  in  miles?  Do  we  observe  the  horizontal  paral- 
lax of  a  remote  planet,  or  compute  it  ? 


Mercury, 

-     0.3871  " 

Venus,     - 

-  0.7233 

Earth,  - 

-      1.0000 

Mars, 

1.5237 

Jupiter, 

-     5.2028 

Saturn,     - 

-  9.5388 

Uranus, 

-     19.1824  , 

126          ELEMENTARY  ASTRONOMY. 

greater  distance,  the  angle  must  be  proportionally  less.  Seen 
from  a  distance  equal  to  the  mean  distance  of  Jupiter  from  the 

o"  r» 

sun,  the  angle  would  be  -  -  --     This,  then,  is  the  horizontal 
5.2028 

parallax  of  Jupiter,  when  Jupiter  is  at  a  distance  from  the  earth 
equal  to  the  mean  distance  of  Jupiter  from  the  sun.  The  appa- 
rent semi-diameter  of  Jupiter,  when  at  the  same  distance,  as 
determined  by  observation,  is  18".35  ;  therefore  the  diameter  of 
Jupiter  can  be  determined  by  the  following  proportion 

7912  :   D  :  :       8'6       :  18.35, 
5.2028 

in  which  D  represents  the  magnitude  sought. 


Whence  D:  =7912*11  .1=87823  miles 

8.6 

In  the  same  manner  we  can  find  the  diameter  of  any  other 
planet  whose  apparent  diameter  can  be  distinctly  measured, 
and  whose  relative  distance  to  the  sun  is  known.  The  diameter 
may  also  be  computed  directly  by  plane  trigonometry. 

We  have  just  seen  that  the  diameter  of  Jupiter  is  11.1  times 
the  diameter  of  the  earth  ;  but  this  is  the  equatorial  diameter 
of  the  planet.  Its  polar  diameter  is  less,  in  the  proportion  of 
167  to  177,  as  determined  by  the  mean  of  many  micrometrical 
measurements  ;  which  proportion  gives  82930  miles,  for  the 
polar  diameter  of  Jupiter.  These  extremes  give  the  mean 
diameter  of  Jupiter,  to  the  mean  diameter  of  the  earth,  as 
10.8  to  1. 

But  the  magnitudes  of  similar  bodies  are  to  one  another  as 
the  cubes  of  their  like  dimensions  ;  therefore  the  magnitude  of 
Jupiter  is  to  that  of  the  earth,  as  (10.8)3  to  1,  and  from  thence 
we  learn  that  Jupiter  is  1260  times  greater  than  the  earth. 

In  this  manner  are  found  the  magnitudes,  distances,  velocity, 
&c.  &c.  of  the  planets,  which  appear  in  tables  in  various  astro- 
nomical works. 

State  the  proportion  to  find  the  diameter  of  a  planet  when  its  horizontal 
parallax  and  apparent  semi-diameter  are  both  known.  How  much  greater 
is  the  diameter  of  Jupiter  than  the  earth  ?  How  much  greater  then  is  the 
magnitude  of  Jupiter  than  that  of  the  earth? 


DESCRIPTION  OF  THE  SOLAR  SYSTEM.  127 


CHAPTER   IX. 

A   GENERAL  DESCRIPTION    OF    THE    SOLAR 
SYSTEM. 

THE  solar  system  is  so  called  because  theK  sun  occupies  the 
Central  position,  and  apparently  holds  and  governs  the  motion 
of  all  the  planets  which  revolve  around  him. 

We  shall  commence  our  description  with 

THE     SUN. 

This  body,  as  we  have  seen  in  the  preceding  pages,  is  of 
immense  magnitude,  much  greater  than  all  the  planets  taken 
together,  comparatively  stationary,  the  dispenser  of  light  and 
heat,  and  apparently  at  least,  the  repository  of  that  attractive 
force  which  holds  the  system  together,  and  regulates  the  plan- 
etary motions. 

"Spots  on  the  sun  seem  first  to  have  been  observed  in  the 
year  1611,  since  which  time  they  have  constantly  attracted 
attention,  and  have  been  the  subject  of  investigation  among 
astronomers/' 

A  spot  first  appears  on  the  eastern  limb  of  the  sun,  and  by 
degrees  comes  forward  to  the  middle,  and  passes  off  to  the  west. 
After  being  absent  about  the  same  length  of  time,  the  same 
spot  appears  in  the  same  place  as  before,  thus  indicating  a  revo- 
lution of  the  sun  on  an  axis,  in  25  days  14  hours,  the  sy nodical 
revolution  of  the  spots  being  27  days  12*-  hours. 

These  spots  change  their  appearance,  "and  become  greater 
or  less,  to  an  observer  on  the  earth,  as  they  are  turned  to,  or 
from  him  ;  they  also  change  in  respect  to  real  magnitude  and 
number;  one  spot,  seen  by  Dr.  Herschel,  was  estimated  to  be 

Whereabouts  in  the  solar  system  is  the  sun  ?  Does  it  revolve  on  an  axis 
—  and  if  so,  how  did  the  fact  become  known  ?  AV  hat  is  the  time  of  revo- 
lution ?  What  is  said  of  the  size  of  some  of  these  spots  ? 


128  ELEMENTARY  ASTRONOMY. 

more  than  six  times  the  size  of  our  earth,  being  50000  miles 
in  diameter.  Sometimes  forty  or  fifty  spots  may  be  seen  at  the 
same  time,  and  sometimes  only  one.  They  are  often  so  large 
as  to  be  seen  with  the  naked  eye;  this  was  the  case  in  1816. 

"  In  two  instances,  these  spots  have  been  seen  to  burst  into 
several  parts,  and  the  parts  to  fly  in  several  directions,  like  a 
piece  of  ice  thrown  upon  the  ground. 

"Dr.  Herschel,  from  many  observations  with  his  great  tel- 
escope, concludes^  that  the  shining  matter  of  the  sun  consists 
of  a  mass  of  phosphoric  clouds,  and  that  the  spots  on  his  sur- 
face are  owing  to  disturbances  in  the  equilibrium  of  this  lumi- 
nous matter,  by  which  openings  are  made  through  it.  There 
are,  however,  objections  to  this  theory,  as  indeed  there  are  to 
all  the  others,  and  at  present  it  can  only  be  said,  that  no  satis- 
factory explanation  of  the  cause  of  these  spots  has  been  given." 

MERCURY. 

This  planet  is  the  nearest  to  the  sun,  and  has  been  the  sub- 
ject of  considerable  remark  in  the  preceding  pages.  It  is 
rarely  visible,  owing  to  its  small  size  and  proximity  to  the  sun, 
and  it  never  appears  larger  to  the  naked  eye  than  a  star  of  the 
fifth  magnitude. 

Mercury  is  seen  through  a  telescope  sometimes  in  the  form 
of  a  half  moon,  and  sometimes  a  little  more  or  less  than  half 
its  disc  is  seen ;  hence  it  is  inferred,  that  it  has  the  same  phases 
as  the  moon,  except  that  it  never  appears  quite  round,  because 
its  enlightened  side  is  never  turned  directly  towards  us,  unless 
when  it  is  so  near  the  sun  as  to  become  invisible,  by  reason 
of  the  splendor  of  the  sun's  rays.  The  enlightened  side  of 
this  planet  being  always  towards  the  sun,  and  its  never  appear- 
ing round,  are  evident  proofs  that  it  shines  not  by  its  own 
light;  for,  if  it  did,  it  would  constantly  appear  round.  The 
best  observations  of  this  planet  are  those  made  when  it  is 
seen  on  the  sun's  disc,  called  its  transit ;  for  in  its  lower  con- 
How  large  does  Mercury  appear  ?  What  is  its  position  when  the  best 
observations  can  be  made  on  it  ? 


DESCRIPTION  OF  THE  SOLAR  SYSTEM.  129 

junction,  he  sometimes  passes  before  the  sun,  like  a  little  spot, 
eclipsing  a  small  part  of  the  sun's  body. 

Mercury  is  too  near  the  sun  to  admit  of  any  observations  on 
the  spots  on  its  surface ;  but  its  period  of  rotation  has  been 
determined  by  the  variations  in  its  horns  —  the  same  ragged 
corner  comes  round  at  regular  intervals  of  time  —  24h.  5m. 

The  best  time  to  see  Mercury,  in  the  evening,  is  in  the  spring 
of  the  year,  when  the  planet  is  at  its  greatest  elongation  east  of 
the  sun.  It  will  then  be  visible  to  the  naked  eye  about  fifteen 
minutes,  and  will  set  about  an  hour  and  fifty  minutes  after  the 
sun.  When  the  planet  is  west  of  the  sun,  and  at  its  greatest 
distance,  it  may  be  seen  in  the  morning,  most  advantageously 
in  August  and  September.  The  symbol  for  the  greatest  elon- 
gation of  Mercury,  as  written  in  the  common  almanac,  is  §  Gr. 
Elon. 

VENUS. 

This  planet  is  second  in  order  from  the  sun,  and  in  relation 
to  its  position  and  motion,  it  has  been  sufficiently  described. 
The  period  of  its  rotation  on  its  axis  is  23h.  21m.  The  position 
of  the  axis  is  always  the  same,  and  is  not  at  right  angles  to  the 
plane  of  its  orbit,  which  gives  it  a  change  of  seasons.  The 
tangent  position  of  the  sun's  light  across  this  planet  shows  a 
very  rough  surface  ;  indeed,  high  mountains.  By  the  radiating 
and  glimmering  nature  of  the 
light  of  this  planet,  we  infer 
that  it  must  have  a  deep  and 
dense  atmosphere. 

These  figures  present  a  tele- 
scopic view  of  this  planet ;  the 
narrow  crescent  appears    when 
the  planet  is  near  its  inferior  conjunction,  the  other  when  the 
planet  is  near  its  greatest  elongation. 

The  enlightened  side  is  always  towards  the  sun,  which  shows 

How  was  the  revolution  of  Mercury,  on  an  axis,  determined  ?  Does 
Venus  revolve  on  an  axis,  and  in  what  tijne  ? 


130  ELEMENTARY  ASTRONOMY. 

that  it  shines  not  by  its  own  light,  but  by  reflecting  the  light 
from  the  sun ;  and  indeed,  observations  show  that  this  is  true 
of  all  the  planets.  For  the  magnitude,  motion,  inclination  of 
orbit,  &c.  of  Venus,  see  tables. 

THE     EARTH 

Is  the  next  planet  in  ike  system  ;  but  it  would  be  only  for- 
mality to  give  any  description  of  it  in  this  connection.  As  a 
planet,  it  seems  to  be  highly  favored  above  its  neighboring 
planets,  by  being  furnished  with  an  attendant,  the  moon  ;  and 
insignificant  as  this  latter  body  is,  compared  to  the  whole  solar 
system,  it  is  the  most  important  to  the  inhabitants  of  our  earth. 
The  two  bodies,  the  earth  and  the  moon,  as  seen  from  the  sun, 
are  very  small :  the  former  subtending  an  angle  of  about  17" 
in  diameter,  and  the  latter  about  4",  and  their  distance  asunder 
never  greater  than  between  seven  and  eight  minutes  of  a  degree. 
We  shall  give  a  particular  description  of  the  moon,  its  orbit, 
motion,  &c.  <fcc.  in  a  future  chapter. 

MARS. 

The  fourth  planet  from  the  sun  is  Mars  ;  its  orbit  is  nearest 
the  orbit  of  the  earth,  or  it  is  the  first  superior  planet.  It  is 
of  a  fiery  red  color,  and  very  variable  in  its  apparent  magni- 
tude corresponding  with  its  va- 
riable distance.  About  every 
other  year,  when  it  comes  to 
the  meridian  near  midnight,  it 
is  then  most  conspicuous  ;  and 
the  next  year  it  is  scarcely  no- 
ticed by  the  common  observer. 
The  figure  in  the  margin 
represents  the  telescopic  ap- 
pearance of  Mars  when  its  ap- 
parent magnitude  is  greatest,  near  its  opposition  to  the  sun. 

Does  Venus  shine  by  its  own  light?  and  if  not,  how  is  that  fact  known? 
What  heavenly  body  is  most  important  to  the  inhabitants  of  the  earth, 
(the  sun  excepted)?  What  is  the  position  of  Mars  in  the  solar  system? 
Describe  that  planet.  Why  is  it  much  more  conspicuous  sometimes  than 
others?  When  most  conspicuous,  what  is  its  position  in  respect  to  the  sun? 


DESCRIPTION  OF  THE  SOLAR  SYSTEM.  131 

"The  physical  appearance  of  Mars  is  somewhat  remarkable. 
His  polar  regions,  when  seen  through  a  telescope,  have  a  bril- 
liancy so  much  greater  than  the  rest  of  his  disc,  that  there  can 
be  little  doubt  that,  as  with  the  earth  so  with  this  planet,  accu- 
mulations of  ice  or  snow  take  place  during  the  winters  of  those 
regions.  In  1781  the  south  polar  spot  was  extremely  bright  ; 
for  a  year  it  had  not  been  exposed  to  the  solar  rays.  The  color 
of  the  planet  most  probably  arises  from  a  dense  atmosphere 
which  surrounds  him,  of  the  existence  of  which  there  is  other 
proof  depending  on  the  appearance  of  stars  as  they  approach 
him ;  they  grow  dim  and  are  sometimes  wholly  extinguished 
as  their  rays  pass  through  that  medium." 

The  next  planet  known  to  ancient  astronomers,  is  Jupiter ; 
but  its  distance  is  so  great  beyond  the  orbit  of  Mars,  that  the 
void  space  between  the  two  had  often  been  ^considered  as  an 
imperfection,  and  it  was  a  general  impression  among  astrono- 
mers that  a  planet  ought  to  occupy  that  vacant  space. 

For  complete  symmetry  in  the  solar  system,  a  planet  ought 
to  exist  at  about  2.8  distance  from  the  sun,  calling  the  distance 
of  the  earth  unity,  and  that  planet  two  or  three  times  the  mag- 
nitude of  the  earth,  —  but  certainly  no  such  planet  existed,  for 
such  an  one  could  not  possibly  have  escaped  observation. 

Mere  human  reason  had  long  decided  that  a  planet  ought  to 
exist  in  this  void  space,  and  in  this  case,  reason  has  triumphed. 
On  the  1st  of  January,  1801,  M.  Piazzi,  an  astronomer  of  Pa- 
lermo, in  Sicily,  discovered  a  small  planet,  which  he  called 
Ceres,  which  was  soon  found  to  occupy  this  very  vacant  space. 
This  set  other  astronomers  on  the  alert,  and  three  other  small 
planets  were  discovered  between  January,  1801,  and  April, 
1807.  The  following  table  gives  much  information  in  a  very 
small  compass : 


Planets. 

Names  of  Dis- 
coverers. 

Residence  of  Discoverers. 

Date  of  Discovery. 

Ceres, 
Pallas, 
Juno, 

Vesta, 

M.  Piazzi, 
Dr.  Gibers, 
M.  Harding, 
Dr.  Olbers, 

Palermo,  Sicily, 
Bremen,  Germany, 
Lilienthal,  near  Bremen, 
Bremen, 

1st  January,  1801. 
28th  March,  1802. 
1st  September,  1804. 
29th  March,  1807. 

For  complete  symmetry,  -whereabouts  in  the  solar  system  should  a  large 
planet  exist  ?    When  was  the  first  planet  discovered  in  that  space  ? 


132  ELEMENTARY  ASTRONOMY. 

These  planets  revolving  at  nearly  the  same  mean  distance 
from  the  sun,  and  performing  their  revolutions  in  times  of  near 
the  same  duration  —  and  being  very  small,  Dr.  Olbers  suggested 
that^hey  might  be  but  fragments  of  one  large  planet  that  burst 
asunder  by  its  internal  fires. 

This  bold  and  original  idea  was  received  as  visionary,  and 
by  some,  with  sneers,  as  all  bold  and  original  ideas  always 
have  been  received  at  first,  but  time  and  reflection  have  grad- 
ually brought  this  theory  into  favor. 

If  a  planet  has  really  burst,  it  is  but  reasonable  to  suppose 
that  it  separated  into  many  fragments ;  and,  agreeably  to  this 
view  of  the  subject,  astronomers  have  been  constantly  on  the 
alert  for  new  planets,  in  the  same  regions  of  space  ;  and  every 
discovery  of  the  kind  greatly  increases  the  probability  of  the 
theory. 

On  the  8th  of  December,  1845,  Mr.  Hencke,  of  Dresden, 
discovered  a  planet  called  Astrea,  and  the  same  observer  dis- 
covered another  in  1847,  called  Hebe. 

The  success  of  Mr.  Hencke  induced  others  to  like  examina- 
tions in  the  heavens,  and  Mr.  Hind,  of  London,  in  1848,  dis- 
covered two  other  planets,  Iris  and  Flora. 

Since  this  time,  seven  other  small  planets  have  been  dis- 
covered, Egeria,  Eunomia,  Irene,  Metis,  Parthenope,  Hygeria, 
and  Victoria.  Thus,  we  have  ffteen*  miniature  worlds,  all 
located  in  that  space  where  reason  called  for  a  planet ;  and,  is 
it  unreasonable  then  to  suppose  that  these  fifteen,  and  perhaps 
others  yet  unseen,  are  but  fragments  of  a  planet  ?  all  of  them 
together  would  not  make  one  planet  larger  than  the  earth. 

*  This  chapter  was  written  in  1854,  since  which  time,  and  up  to  the 
present,  some  seventeen  others  have  been  added  to  the  list.  At  this  time, 
1857,  thirty-one  have  been  tabulated  in  the  Nautical  Almanac;  but  all  of 
them  put  together  would  not  make  a  very  large  planet,  and  they  are  of  no 
interest  to  readers  of  this  work.  We  have  tabulated  some  on  the  next  page. 

On  finding  four  planets  in  this  region,  what  theory  was  advanced  by 
Dr.  Olbers  ?  Is  it  reasonable  to  suppose  that  all  of  these  small  bodies  at 
about  the  same  mean  distance  from  the  sun,  could  be  originally  distinct 
and  independent  planets  | 


DESCRIPTION  OF  THE  SOLAR  SYSTEM. 


133 


For  further  information,  we  give  the  following  tabular  facts, 
which  will  be  verified,  or  modified  and  corrected,  by  subse- 
quent observations : 


Planets. 

Mean   dis- 
tance from 
the  sun. 

Mean  time 
of  Revolu- 
tion. 

Eccentricity 
of  orbits. 

Lon.of  the 
Ascending 
node. 

Inclination 
of  orbit. 

Earth's  dis.  ] 

Days. 

To  Ecliptic. 

Flora, 

2.2014 

1193.16 

0.15677 

110°  21' 

5°  53' 

Victoria, 

2.3348 

1303.08 

0.21854 

235°  40' 

8°  23' 

*Vesta, 

2.3627 

1326.26 

0.08945 

103°  24' 

7°    8' 

Iris, 

2.3858 

1345.66 

0.23232 

259°  44' 

5°  28' 

Metis, 

2.3868 

1346.90 

0.12274 

68°  28' 

5°  36' 

Hebe, 

2.4256 

1379.68 

0.20200 

138°  32' 

14°  47' 

Parthenope, 

2.4483 

1399.06 

0.09800 

125°    0' 

4°  37' 

Irene, 

2.5805 

1515.40 

0.16974 

86°  51' 

9°    6' 

Astrea, 

2.6173 

1547.58 

0.18880 

141°  28 

5°  19' 

Egeria, 

2.5829 

1515.82 

0.08628 

43°  18' 

16°  33' 

*Juno, 

2.6679 

1591.68 

0.25637 

170°  58' 

13°    3' 

*  Ceres, 

2.7653 

1679.86 

0.07904 

80°  49' 

10°  36' 

*Pallas, 

2.7715 

1686.22 

0.23894 

172°  37' 

34°  42' 

Eunomia, 

2.6483 

1574.08 

0.18856 

293°  54' 

11°  44' 

Hygeia, 

3.1512 

2043.38 

0.10090 

287°  38' 

3°  47' 

Psyche, 

2.9771 

1834.61 

0.13082 

150°  36' 

3°    4' 

Fortuna, 

2.5342 

1440.80 

0.17023 

211°  17' 

1°  32' 

Melpomene, 

2.3292 

1269.81 

0.21644 

150°    0' 

10°    9' 

Thetis, 

2.4718 

1419.31 

0.12736 

125°  25' 

5°  35' 

Lutetia, 

2.4353 

1387.77 

0.16104 

80°  34' 

3°    5' 

Calliope, 

2.9054 

1809.00 

0.10308 

66°  38' 

13°  45' 

Amphitrite, 

2.5521 

1489.22 

0.06716 

356°  27' 

6°    8' 

The  hypothesis  that  the  small  planets,  Ceres  and  Pallas, 
were  originally  one  planet,  and  must,  therefore,  by  the  laws  of 
motion  and  inertia,  have  two  common  points  in  the  heavens, 
near  which  all  of  them  must  pass,  led  to  the  discovery  of  Juno 
and  Vesta,  by  carefully  observing  in  these  two  portions  of  the 
heavens  for  other  fragments  which  might  exist ;  and  as  this 
theory  came  more  and  more  into  favor,  observations  were  made 

*  We  made  an  effort  to  arrange  these  planets  in  the  order  of  their 
distances  from  the  sun,  and  we  have  done  so,  as  far  as  Hygeia.  The  fol- 
lowing ones  were  subsequent  discovei'ies.  Some  future  day,  when  these 
elements  will  be  better  known,  by  more  varied  and  extended  observations, 
a  re-arrangement  can  be  made. 


134  ELEMENTARY  ASTRONOMY. 

with  greater  and  greater  care,  and  the  result  has  been,  these 
recent  interesting  and  singular  discoveries. 

The  apparent  diameters  of  these  planets  are  too  small  to  be 
accurately  measured ;  and  therefore  we  have  only  a  very  rough 
or  conjectural  knowledge  of  their  diameters. 

All  of  these  planets  are  invisible  to  the  naked  eye,  except 
Vesta,  which  sometimes  can  be  seen  as  a  star  of  the  5th  or  6th 
magnitude. 

The  fact  that  these  bodies  have  never  caused  any  sensible 
perturbations  in  the  motion  of  Mars,  is  a  physical  demonstra- 
tion that  they  must  be  very  small,  separately  considered,  and 
their  aggregate  influence  must  be  nearly  frittered  away,  in 
consequence  of  their  dispersed  positions. 

JUPITER. 

We  now  come  to  the  most  magnificent  planet  in  the  system 
—  the  well-known  Jupiter  —  which  is  nearly  1300  times  the 
magnitude  of  the  earth. 

The  disc  of  Jupiter  is  always  observed  to  be  crossed,  in  an 
eastern  and  western  direction,  by  dark  bands,  as  represented 
in  the  annexed  figure. 


What  is  said  of  the  diameters  and  real  magnitudes  of  these  planets? 
Which  planet  is  the  most  magnificent  in  the  system  ? 


DESCRIPTION  OF  THE  SOLAR  SYSTEM.  135 

"These  belts  are,  however,  by  no  means  alike  at  all  times ; 
they  vary  in  breadth  and  in  situation  on  the  disc  (though  never 
in  their  general  direction).  They  have  even  been  seen  broken 
up,  and  distributed  over  the  whole  face  of  the  planet :  but  this 
phenomenon  is  extremely  rare.  Branches  running  out  from 
them,  and  subdivisions,  as  represented  in  the  figure,  as  well  as 
evident  dark  spots,  like  strings  of  clouds,  are  by  no  means 
uncommon;  and  from  these,  attentively^  watched,  it  is  con- 
cluded that  this  planet  revolves  in  the  surprisingly  short  period 
of  9h.  55m.  50s.  (sid.  time),  on  an  axis  perpendicular  to  the 
direction  of  the  belts.  Now,  it  is*very  remarkable,  and  forms 
a  most  satisfactory  comment  on  the  reasoning  by  which  the 
spheroidal  figure  of  the  earth  has  been  deduced  from  its  diur- 
nal rotation,  that  the  outline  of  Jupiter's  disc  is  evidently  not 
circular,  but  elliptic,  being  considerably  flattened  in  the  direc- 
tion of  its  axis  of  rotation. 

"The  parallelism  of  the  belts  to  the  equator,  of  Jupiter, 
their  occasional  variations,  and  the  appearances  o.f  spots  seen 
upon  them,  render  it  extremely  probable  that  they  subsist  in 
the  atmosphere  of  the  planet,  forming  tracts  of  comparatively 
clear  sky,  determined  by  currents  analogous  to  our  tradewinds, 
but  of  a  much  more  steady  and  decided  character,  as  might 
indeed  be  expected  from  the  immense  velocity  of  its  rotation. 
That  it  is  the  comparatively  darker  body  of  the  planet  which 
appears  in  the  belts,  is  evident  from  this, — that  they  do  not 
come  up  in  all  their  strength  to  the  edge  of  the  disc,  but  fade 
away  gradually  before  they  reach  it. 

"  When  Jupiter  is  viewed  with  a  telescope,  even  of  moderate 
power,  it  is  seen  accompanied  by  four  small  stars,  nearly  in  a 
straight  line  parallel  to  the  ecliptic.  These  always  accompany 
the  planet,  and  are  called  its  Satellites.  They  are  continually 

In  what  time  does  Jupiter  revolve  on  its  axis?  Those  dark  belts  on 
Jupiter,  are  they  on  the  body  of  the  planet,  or  are  they  probably  clouds 
in  its  atmosphere  ?  Is  Jupiter  exactly  spherical  ?  How  many  moons 
has  Jupiter? 


136          ELEMENTARY  ASTRONOMY. 

changing  their  positions  with  respect  to  one  another,  and  to  the 
planet,  being  sometimes  all  to  the  right,  and  sometimes  all  to 
the  left ;  but  more  frequently  some  on  each  side.  The  greatest 
distances  to  which  they  recede  from  the  planet,  on  each  side, 
are  different  for  the  different  satellites,  and  they  are  thus  dis- 
tinguished :  that  being  called  the  First  satellite,  which  recedes 
to  the  least  distance  ;  that  the  Second,  which  recedes  to  the 
next  greater  distance,  and  so  on.  The  satellites  of  Jupiter 
were  discovered  by  Galileo,  in  1610. 

"  Sometimes  a  satellite  is  observed  to  pass  between  the  sun 
and  Jupiter,  and  to  cast  a  shadow  which  describes  a  chord 
across  the  disc.  This  produces  an  eclipse  of  the  sun,  to  Jupi- 
ter, analogous  to  those  which  the  moon  produces  on  the  earth. 
It  follows  that  Jupiter  and  its  satellites  are  opake  bodies,  which 
shine  by  reflecting  the  light  of  the  sun. 

"  Careful  and  repeated  observations  show  that  the  motions 
of  the  satellites  are  from  west  to  east,  in  orbits  nearly  circular, 
and  making  small  angles  with  the  plane  of  Jupiter's  orbit. 
Observations  on  the  eclipses  of  the  satellites  make  known  their 
synodic  revolutions,  from  which  their  sidereal  revolutions  are 
easily  deduced.  From  measurements  of  the  greatest  apparent 
distances  of  the  satellites  from  the  planet,  their  real  distances 
are  determined. 

"  A  comparison  of  the  mean  distances  of  tjie  satellites,  with 
their  sidereal  revolutions,  proves  that  Kepler's  third  law,  with 
respect  to  the  planets,  applies  also  to  the  satellites  of  Jupiter. 
The  squares  of  their  sidereal  revolutions  are  as  the  cubes  of 
their  mean  distances  from  the  planet. 

"  The  planets  Saturn  and  Uranus  are  also  attended  by  satel- 
lites, and  the  same  law  has  place  with  them." 

By  the  eclipses  of  Jupiter's  satellites,  the  progressive  nature 

Do  the  revolutions  of  these  moons  correspond  to  Kepler's  third  law?  Re- 
peat the  law.  What  discovery  was  made  in  relation  to  light,  by  the  aid 
of  the  eclipses  of  Jupiter's  moons  ?  Explain  this  by  a  figure  on  the  black 
board. 


DESCRIPTION  OF  THE  SOLAR  SYSTEM.  137 

of  light  was  discovered  ;   which  we  illustrate  in  the  following 
manner : 


Let  S  represent  the  sun,  J  Jupiter,  E  Earth,  and  m  Jupiter's 
first  satellite.  By  careful  and  accurate  observations  astrono- 
mers have  decided  that  the  mean  revolution  of  this  satellite 
round  its  primary,  is  performed  in  42h.  28m.  and  35s.;  that  is, 
the  mean  time  from  one  eclipse  to  another. 

But  when  the  earth  is  at  E,  and  moving  in  a  direction  to- 
ward, or  nearly  toward,  the  planet  as  represented  in  the  figure, 
the  mean  time  between  two  consecutive  eclipses  is  shortened 
about  fifteen  seconds  ;  and  we  can  explain  this  on  no  other 
hypothesis  than  that  the  earth  has  advanced  and  met  the  suc- 
cessive progression  of  light.  When  the  earth  is  in  position  as 
respects  the  sun  and  Jupiter,  as  represented  in  our  figure  at  E"9 
and  moving  from  Jupiter,  then  the  interval  between  two  con- 
secutive eclipses  of  Jupiter's  first  satellite  is  prolonged  or 
increased  about  fifteen  seconds. 

But  during  the  interval  of  one  revolution  of  Jupiter's  first 
satellite,  the  earth  moves  in  its  orbit  about  2880000  miles ; 
this,  divided  by  15,  gives  192000  miles  for  the  motion  of  light 
in  one  second  of  time  ;  and  this  velocity  will  carry  light  from 
the  sun  to  the  earth  in  about  eight  and  one-fourth  minutes. 

As  an  eclipse  of  one  of  Jupiter's  satellites  may  be  seen  from 
all  places  where  the  planet  is  then  visible,  two  observers  view- 
ing it  will  have  a  signal  for  the  same  moment,  at  their  respective 

How  do  astronomers  find  the  difference  of  longitude  between  two  places 
by  means  of  the  eclipses  of  Jupiter's  satellites  ? 
12 


138  ELEMENTARY  ASTRONOMY. 

places  ;  and  their  difference  in  local  time,  will  give  their  dif- 
ference in  longitude.  For  example,  if  one  observer  saw  one 
of  these  eclipses  at  lOh.  in  the  evening,  and  another  at  8h. 
30m.,  the  difference  of  longitude  between  the  observers  would 
be  lh.  30m.  in  time,  or  22°  30'  of  arc. 

The  absolute  time  that  the  eclipse  takes  place,  is  the  same 
to  all  observers  ;  and  he  who  has  the  latest  local  time  is  the 
most  eastward. 

These  eclipses  cannot  be  observed  at  sea,  by  reason  of  the 
motion  of  the  vessel.  The  telescope  cannot  be  held  sufficiently 
steady. 

S ATU  RN . 

The  next  planet  in  order  of  remoteness  from  the  sun,  is 
Saturn,  the  most  wonderful  object  in  the  solar  system.  Though 
less  than  Jupiter,  it  is  about  79000  miles  in  diameter,  and  1000 
times  greater  than  our  earth. 

"  This  stupendous  globe,  besides  being  attended  by  no  less 
than  seven  satellites,  or  moons,  is  surrounded  with  two  broad, 
flat,  extremely  thin  rings,  concentric  with  the  planet  and  with 
each  other ;  both  lying  in  one  plane,  and  separated  by  a  very 
narrow  interval  from  each  other  throughout  their  whole  cir- 
cumference, as  they  are  from  the  planet  by  a  much  wider. 
The  dimensions  of  this  extraordinary  appendage  are  as  follows : 

Miles. 

Exterior  diameter  of  exterior  ring, ,   =   17641 8 

Interior  ditto, =   155272 

Exterior  diameter  of  interior  ring, =   1 51 690 

Interior  ditto, =   117339 

Equatorial  diameter  of  the  body, =     79160 

Interval  between  the  planet  and  interior  ring,. .    =     19090 

Interior  of  the  rings, =        1791 

Thickness  of  the  rings  not  exceeding =          100 

Can  these  eclipses  be  used  at  sea?  Why  not?  What  is  the  next  planet 
in  the  system  ?  What  is  the  magnitude  of  Saturn  ?  What  is  there  re- 
markable about  the  planet  ?  How  many  moons  has  it  ? 


DESCRIPTION  OF  THE  SOLAR  SYSTEM.  139 

"  The  figure  represents  Saturn  surrounded  by  its  rings,  and 
having  its  body  striped  with  dark  belts,  somewhat  similar,  but 


broader  and  less  strongly  marked  than  those  of  Jupiter,  and 
owing,  doubtless,  to  a  similar  cause.  That  the  ring  is  a  solid 
opake  substance,  is  shown  by  its  throwing  its  shadow  on  the 
body  of  the  planet,  on  the  side  nearest  the  sun,  and  on  the 
other  side  receiving  that  of  the  body,  as  shown  in  the  figure. 
From  the  parallelism  of  the  belts  with  the  plane  of  the  ring,  it 
may  be  conjectured,  that  the  axis  of  rotation  of  the  planet  is 
perpendicular  to  that  plane ;  and  this  conjecture  is  confirmed 
by  the  occasional  appearance  of  extensive  dusky  spots  on  its 
surface,  which  when  watched,  like  the  spots  on  Mars  or  Jupiter, 
indicate  a  rotation  in  lOh.  29m.  17s.  about  an  axis  so  situated. 
"  It  will  naturally  be  asked  how  so  stupendous  an  arch,  if 
composed  of  solid  and  ponderous  materials,  can  be  sustained 
without  collapsing  and  falling  in  upon  the  planet  ?  The  answer 
to  this  is  to  be  found  in  a  swift  rotation  of  the  ring,  in  its  own 
plane,  which  observation  has  detected,  owing  to  some  portions 
of  the  ring  being  a  little  less  bright  than  others,  and  assigned 
its  period  at  lOh.  29m.  17s.,  which,  from  what  we  know  of  its 
dimensions,  and  of  the  force  of  gravity  in  the  Saturnian  sys- 
tem, is  very  nearly  the  periodic  time  of  a  satellite  revolving  at 
the  same  distance  as  the  middle  of  its  breadth.  It  is  the  cen- 
trifugal force,  then,  arising  from  this  rotation,  which  sustains 
it ;  and,  although  no  observation  nice  enough  to  exhibit  a 

Which  is  most  probable,  that  the  rings  are  solid,  or  consist  of  vapor  ? 
Do  the  rings  revolve  ?    In  what  length  of  time  ? 


HO          ELEMENTARY  ASTRONOMY. 

difference  of  periods  between  the  outer  and  inner  rings,  have 
hitherto  been  made,  it  is  more  than  probable  that  such  a  dif- 
ference does  exist,  so  as  to  place  each,  independently  of  the  other, 
in  a  similar  state  of  equilibrium. 

"  Although  the  rings  are,  as  we  have  said,  very  nearly  con- 
centric with  the  body  of  Saturn,  yet  recent  micrometrical 
measurements,  of  extreme  delicacy,  have  demonstrated  that 
the  coincidence  is  not  mathematically  exact,  but  that  the 
center  of  gravity  of  the  rings  oscillates  round  that  of  the  body, 
describing  a  very  minute  orbit,  probably  under  laws  of  much 
complexity.  Trifling  as  this  remark  may  appear,  it  is  of  the 
utmost  importance  to  the  stability  of  the  system  of  the  rings. 
Supposing  them  mathematically  perfect  in  their  circular  form, 
and  exactly  concentric  with  the  planet,  it  is  demonstrable  that 
they  would  form  (in  spite  of  their  centrifugal  force)  a  system 
in  a  state  of  unstable  equilibrium,  which  the  slightest  external 
power  would  subvert  —  not  by  causing  a  rupture  in  the  sub- 
stance of  the  rings  —  but  by  precipitating  them,  unbroken,  on 
the  surface  of  the  planet.  For  the  attraction  of  such  a  ring  or 
rings  on  a  point  or  sphere  eccentrically  situate  within  them,  is 
not  the  same  in  all  directions,  but  tends  to  draw  the  point  or 
sphere  toward  the  nearest  part  of  the  ring,  or  away  from  the 
center.  Hence,  supposing  the  body  to  become,  from  any  cause, 
ever  so  little  eccentric  to  the  ring,  the  tendency  of  their  mu- 
tual gravity  is,  not  to  correct,  but  to  increase  this  eccentricity, 
and  to  bring  the  nearest  parts  of  them  together." 
URA  NU  s . 

This  planet,  the  next  beyond  Saturn,  was  discovered  by  Sir 
W.  F.  Herschel,  in  1781,  and,  for  a  time,  was  called  Herschel, 
in  honor  of  its  discoverer ;  but,  according  to  custom,  the  name 
of  a  heathen  deity  has  been  substituted,  and  the  planet  is  now 
called  Uranus — the  father  of  Saturn. 

Is  it  probable  that  the  rings  revolve  around  Saturn,  as  moons  in  orbits 
slightly  eccentric  ?  Is  this  necessary  to  preserve  the  existence  of  the  rings 
unbroken  ?  What  is  the  next  planet  in  the  sysiem  V  When,  and  by  whom 
was  it  discovered  ? 


DESCRIPTION  OF  THE  SOLAR  SYSTEM.  141 

This  planet  is  rarely  to  be  seen,  without  a  telescope.  In  a 
clear  night,  and  in  the  absence  of  the  moon,  when  in  a  favor- 
able position  above  the  horizon,  it  may  be  seen  as  a  star  of 
about  the  sixth  magnitude.  Its  real  diameter  is  about  35000 
miles,  and  about  80  times  the  magnitude  of  the  earth. 

The  existence  of  this  planet  was  suggested  by  some  of  the 
perturbations  of  Saturn  ;  which  could  not  be  accounted  for  by 
the  action  of  the  then  known  planets  ;  but  it  does  not  appear 
that  any  computations  were  made,  as  a  guide  to  the  place 
where  the  unknown  disturbing  body  ought  to  exist ;  and,  as  far 
as  we  know,  the  discovery  by  Herschel  was  merely  accidental. 

Not  so  in  respect  to  the  discovery  of  the  most  remote  planet 
now  known  in  the  solar  system  —  the  planet 
NEPTUNE. 

This  planet  was  discovered  in  the  latter  part  of  September, 
1846,  by  a  French  astronomer,  Lererrier;  and  also  a  Mr.  Adams, 
of  Cambridge,  England,  who  has  put  in  his  claim  as  discoverer. 
The  truth  is,  that  the  attention  of  the  astronomers  of  Europe 
had  been  called  to  some  extraordinary  perturbations  of  Uranus; 
which  could  not  be  accounted  for  without  supposing  an  attract- 
ing body  to  be  situated  in  space,  beyond  the  orbit  of  Uranus ; 
and  so  distinct  and  clear  were  these  irregularities,  that  both 
geometers,  Leverrier  and  Adams,  fixed  on  the  same  region  of 
the  heavens,  for  the  then  position  of  their  hypothetical  planet ; 
and  by  diligent  search,  the  planet  was  actually  discovered 
about  the  same  time,  in  both  France  and  England.  All  that  is 
known  of  this  planet  is  comprised  in  the  following  table  : 

Epoch  1852,  Sept.  3d,  mean  time  at  Berlin. 

Mean  longitude,       -  -     341°    1^55")    From  mean 

Longitude  of  the  Perihelion,  47°  16'  36'  >     Equinox. 

Longitude  of  Ascending  Node,      430°    8' 50") 

Inclination  of  the  orbit,  1°  46'  59' 

What  observed  facts  suggested  the  existence  of  Uranus  ?  Was  the  dis- 
covery the  lesult  of  such  an  hypothesis  ?  What  other  planet  was  dis- 
covered by  similar  facts,  and  a  similar  theory  ?  When  and  by  whom  was 
that  planet  discovered  ? 


142  ELEMENTARY  ASTRONOMY. 

Eccentricity  of  the  orbit,     -         -      0.008718 
Mean  daily  sidereal  motion,       -  2l".5545 

Mean  time  of  revolution,  60126.65  days,  or  165  yrs.  nearly. 
Mean  distance  from  the  sun,  30.048,  (the  earth's  distance 
being  unity.)     Future  observations  will  undoubtedly  modify 
and  correct  these  results. 

We  shall  close  this  chapter  with  the  following 'extract  from 
HerschePs  Astronomy,  "which  will  convey  to  the  minds  of  our 
readers  a  general  impression  of  the  relative  magnitudes  and 
distances  of  the  parts  of  our  system.  Choose  any  well-leveled' 
field  or  bowling  green.  On  it  place  a  globe,  two  feet  in  diam- 
eter ;  this  will  represent  the  sun  ;  Mercury  will  be  represented 
by  a  grain  of  mustard  seed,  on  the  circumference  of  a  circle 
164  feet  in  diameter  for  its  orbit;  Venus  a  pea,  on  a  circle  284 
feet  in  diameter;  the  earth  also  a  pea,  on  a  circle  430  feet; 
Mars  a  rather  large  pin's  head,  on  a  circle  of  654  feet ;  Juno, 
Ceres,  Vesta,  and  Pallas,  grains  of  sand,  in  orbits  of  from  1000 
to  1200  feet;  Jupiter  a  moderate-sized  orange,  in  a  circle 
nearly  half  a  mile  across  ;  Saturn  a  small  orange,  on  a  circle 
of  four-fifths  of  a  mile;  and  Uranus  a  full-sized  cherry,  or 
small  plum,  upon  the  circumference  of  a  circle  more  than  a 
mile  and  a  half  in  diameter.  As  to  getting  correct  notions  on 
this  subject  by  drawing  circles  on  paper,  or  still  worse,  from 
those  very  childish  toys  called  orreries,  it  is  out  of  the  ques- 
tion. To  imitate  the  motions  of  the  planets  in  the  above  men- 
tioned orbits,  Mercury  must  describe  its  own  diameter  in  41 
seconds;  Venus,  in  4m.  14s. ;  the  earth,  in  7  minutes  ;  Mars, 
in  4  m.  48s.  ;  Jupiter,  in  2h.  56m.;  Saturn,  in  3h.  13m.;  and 
Uranus,  in  2h.  16m." 

From  this  description  it  will  be  seen  that  the  true  reason 
why  the  solar  system  cannot  be  accurately  represented  on 
paper,  is  this  :  That  if  we  give  the  earth  any  sensible  magni- 
tude, there  will  not  be  space  enough  on  any  paper  to  represent 
th6  sun,  or  to  extend  to  the  planets. 

What  does  Herschel  say  about  representing  the  solar  system  on  paper  ? 
What  term  does  he  apply  to  orreries  ?  Why  can  we  not  make  a  propel 
map  of  the  solar  system  ? 


SECTION  III. 


CHAPTER   I. 

THE    MOON',   ITS  PERIODICAL  REVOLUTIONS, 
AND   APPEARANCES. 

NEXT  to  the  sun,  the  moon  is  the  most  interesting  and  im- 
portant heavenly  body,  to  the  inhabitants  of  the  earth,  and  we 
made  that  a  reason  for  omitting  an  exposition  of  its  motion, 
path,  and  other  phenomena;  until  the  student  acquired  a  little 
astronomical  discipline.  In  Section  II,  chapter  I,  we  have 
explained  parallax  in  general,  and  the  moon's  parallax  in  par- 
ticular, and  found  it  to  vary  from  53'  50"  to  61'  29",  the- amount 
when  the  moon  is  at  its  mean  distance  from  the  earth,  being 
57'  3",  corresponding  to  a  distance  of  60.26  semi-diameters 
from  the  earth. 

The  position  of  the  moon,  in  right  ascension  and  declination, 
can  be  determined  almost  daily,  at  any  observatory,  when  it 
passes  the  meridian  ;  and  before  observatories  were  established, 
the  more  rude  observations  of  its  approximate  positions  among 
the  stars,  from  time  to  time,  were  sufficient  to  establish  its 
periods  with  tolerable  accuracy.  Observations  long  continued, 
have  established  the  fact  that  the  average,  or  mean  time,  of  the 
revolution  of  the  moon  from  the  longitude  of  any  fixed  star  to 
the  longitude  of  the  same  star  again',  is  27  days,  7  hours,  43 
minutes,  1 1  seconds  ;  this  is  called  its  sidereal  revolution.  Its 
revolution  in  respect  to  the  equinoxes  is  7  seconds  less,  because 
the  equinox  itself  runs  back,  or  westward  among  the  stars. 

This  revolution  is  called  the  tropical  revolution. 

• 

What  is  the  moon's  mean  parallax  and  mean  distance  ?  By  what  kind 
of  observations  have  the  moon's  periods  been  established?  What  is  the 
mean  revolution  of  the  moon  ? 


144          ELEMENTARY  ASTRONOMY. 

The  mean  daily  motion  of  the  moon  from  west  to  east  is  13° 
10'  35".  The  mean  daily  motion  of  the  sun,  in  the  same  direc- 
tion is  0°  59'  08",  hence  the  mean  daily  motion  of  the  moon 
exceeds  that  of  the  sun  by  12°  11'  27",  which  will  give  a  revo- 
lution in  29  days  12  hours  44  minutes  and  3  seconds,  which 
is  called  the  synodic  revolution.  This  is  the  average  time 
from  new  moon  to  new  moon  again,  and  from  full  moon  to  full 
moon  again. 

This  interval  is  also  called  a  lunation.  Some  lunations  do 
not  exceed  29  days  and  7  hours,  and  others  come  near  29  days 
and  18  hours. 

The  minimum  lunations  take  place  when  the  moon  changes  a 
day  or  two  after  the  moon  has  passed  its  perigee,  and  the  maxi- 
mum lunations  take  place  when  the  moon  changes  a  day  or  two 
after  the  moon  has  passed  its  apogee.  If  all  lunations  were 
alike  in  length  of  time,  any  one  who  can  work  problems  in 
proportion,  could  compute  the  times  of  new  and  full  moon. 
As  it  is,  the  computations  are  quite  troublesome,  as  every  dis- 
turbing cause  of  motion  has  to  be  separately  considered  and 
allowed  for. 

To  illustrate  one  of  the  principal  causes 
of  the  inequality  of  lunations,  we  give  the 
figure  in  the  margin.  Let  E  be  the  posi- 
tion of  the  earth,  and  CADB  the  moon's 
orbit,  the  moon  moving  in  the  direction 
from  A  to  D  and  from  D  to  B,  and  so  on, 
round  the  ellipse. 

Let  /S'be  the  direction  of  the  sun  ;  then 
when  the  moon  is  near  B,  it  is  in  conjunction 
with  the  sun.     In  27d.  7h.  43m.,  or  there- 
abouts, the  moon  will  be  round  to  the  same  point  B  again,  but 
during  that  time  the  sun  has  apparently  moved  from  S'to  S , 
about  27°,  and  the  moon,  to  come  again  in  range  with  the  sun, 

What  is  the  mean  daily  motion  of  the  moon,  in  "longitude?  What  is 
the  time  from  new  moon  to  new  moon  again  ?  Why  is  this  interval  not 
always  the  same  ?  When  is  the  interval  the  longest  ?  When  the  shortest  T 


LUNAR  MOTIONS.  145 

must  pass  over  about  27°;  but  now,  the  moon  being  at  its 
greatest  distance  from  the  earth,  its  motion  is  much  slower 
than  its  mean  motion,  and  therefore  the  time  required  to  de- 
scribe this  excess  arc,  will  be  greater  than  the  mean  time,  and 
thus  cause  a  long  lunation. 

When  the  new  moon  takes  place  at  B,  the  full  moon  will  take 
place  at  A,  and  along  in  that  part  of  the  moon's  orbit,  the 
excess  arc  will  be  passed  over  by  the  moon  in  less  than  the 
average  time,  and  thus  cause  the  interval  from  full  moon  to 
full  moon  again,  to  be  less  than  the  average  time,  or  a  short 
lunation. 

By  observing  the  moon's  altitude  when  it  comes  on  to  the 
meridian,  from  time  to  time,  it  was  early  ascertained,  that  its 
pathway  through  the  heavens  among  the  stars,  was  not  the 
same  as  that  of  the  sun,  but  that  the  plane  of  its  orbit  was 
inclined  to  the  plane  of  the  ecliptic  by  an  angle  varying  from 
4°  58'  to  5°  18',  the  mean  inclination  being  5°  8';  the  variation 
being  caused  by  the  disturbing  action  of  the  sun's  attraction, 
that  being  different  under  different  circumstances.  The  points 
where  the  moon's  path  crosses  the  ecliptic  (the  sun's  path)  are 
called  the  moon's  nodes;  the  one  where  the  moon  passes  from 
the  south  side  of  the  ecliptic  to  the  north  side,  is  called  the 
ascending  node,  and  the  one  on  the  opposite  side  of  the  sphere 
where  the  moon  crosses  from  the  north  side  of  the  ecliptic  to 
the  south  side,  is  called  the  descending  node.  The  nodes  are  not 
stationary  in  the  heavens  —  they  move  backward  on  the  ecliptic 
on  an  average  of  19°  19'  44"  in  a  year,  which  will  cause  a  com- 
plete revolution  of  the  nodes  in  18  years  228  days  and  9  hours; 

(360°        \ 
) 
19°  19'  44  Y 

This  period  is  nearer  19  than  18  years,  and  it  is  a  period  in 
which  the  path  of  the  moon  through  the  heavens  is  very  nearly 

By  what  observation  was  the  inclination  of  the  moon's  orbit  to  the  eclip- 
tic determined  ?    What  is  that  inclination  ?     What  are  these  points  called 
when  the  moon  crosses  the  ecliptic  ?    Are  these  points  stationary  ?    I* 
what  time,  and  in  what  direction  do  they  make  a  revolution? 
13 


146          ELEMENTARY  ASTRONOMY. 

the  same  as  it  was  19  years  before,  and  it  is  called  the  lunat 
cycle  or  golden  number.*  This  period  has  a  governing  influence 
over  solar  and  lunar  eclipses,  but  we  reserve  that  subject  for 
the  next  chapter. 

When  the  sun  is  in,  or  near  the  moon's  nodes,  its  attraction 
on  the  moon  has  no  tendency  to  draw  the  moon  out  of  the  plane 
of  its  orbit,  and  at  those  times  the  natural  inclination  of  the 
lunar  orbit  to  the  ecliptic  is  about  5°  1 8'.  When  the  sun  is 
90°  from  the  moon's  node,  then  the  inclination  of  the  lunar 
orbit  to  the  ecliptic  is  often  not  more  than  5°,  because  the  ten- 
dency of  the  sun's  attraction  is  then  to  draw  the  moon  towards 
the  ecliptic,  and  this  same  tendency  actually  causes  the  moon 
to  run  into  the  ecliptic  sooner  than  it  otherwise  would,  thus 
producing  a  retrograde  motion  of  the  nodes  themselves. 

The  points  in  the  heavens  where  the  moon  arrives  at  its 
apogee  and  perigee,  are  generally  opposite  to  each  other,  but 
rarely  exactly  so,  —  nor  are  these  points  stationary  in  the 
heavens  —  but  make  a  direct  revolution  in  3231.^^  days, 
nearly  9  years,  —  but  the  true  motion  is  very  variable,  some- 
times backward,  sometimes  forward,  and  sometimes  stationary, 
but  the  forward  or  direct  motion  towards  the  east  prevails, 
making  a  revolution  in  the  time  just  noted. 

The  lunar  apogee  is  much  influenced  by  the  position  of  the 
sun  ;  it  is  dragged  after  the  sun  (so  to  speak),  when  the  sun  is 
a  little  in  advance  of  it,  and  retarded  in  its  motion,  and  even 
retrograde  in  its  motion,  when  the  sun  is  a  little  west  of  it.  In 
short,  the  lunar  orbit  is  not  an  ellipse,  but  resembles  that  figure 
more  nearly  than  any  other,  and  it  is  continually  varying  in  its 
general  eccentricity. 

*  The  Athenians,  433  before  Christ,  inscribed  this  number  in  letters  of 
gold  on  the  walls  of  the  temple  of  Minerva.  Hence  it  is  denominated  the 
GOLDEN  NUMBER. 

What  is  the  golden  number  ?  What  makes  the  period  ?  Why  so  called? 
What  causes  the  retrocession  of  the  nodes?  Is  the  longer  axis  of  the 
moon's  orbit  stationary  in  the  heavens  ?  In  -what  direction  and  in  what 
time  do  the  apogee  and  perigee  points  revolve  ? 


LUNAR  MOTIONS.  147 

The  revolution  of  the  apogee  is  called  the  anomalactic  period. 

The  fact  that  the  same  face  of  the  moon  is  always  towards 
the  earth,  shows  that  it  turns  on  an  axis  in  the  same  time  it 
revolves  round  the  earth,  otherwise  all  sides  oi  it-  would  in  time 
be  presented  to  our  view. 

The  mean  motion  on  its  axis,  and  the  mean  motion  or  revo- 
lution round  the  earth,  is  exactly  the  same,  —  but  the  motion 
on  its  axis  is  uniform,  and  the  motion  in  its  orbit  is  variable, 
and  this  gives  the  face  of  the  moon  an  apparent  vascillating 
motion,  which  is  called  the  moon's  libration. 

There  is  a  lib-ration  in  longitude  caused  by  the  moon's  unequal 
motion  in  longitude,  and  a  libration  in  latitude  caused  by  the 
varying  inclination  of  its  orbit  with  the  ecliptic. 

"  The  moon,  like  the  planets,  is  an  opake  body,  and  shines 
entirely  by  the  light  received  from  the  sun,  a  portion  of  which 
is  reflected  to  the  earth.  As  the  sun  can  only  enlighten  one- 
half  of  a  spherical  surface  at  once,  it  follows  that  according  to 
the  situation  of  an  observer,  with  respect  to  the  illuminated 
part  of  the  moon,  he  will  see  more  or  less  of  the  light  reflected 
from  her  surface.  At  the  conjunction,  or  time  of  new  moon, 
the  moon  is  between  the  earth  and  the  sun,  and  consequently 
that  side  of  the  moon  which  is  never  seen  from  the  earth,  is 
enlightened  by  the  sun;  and  that  side  which  is,  constantly 
turned  towards  the  earth  is  wholly  in  darkness.  Now,  as  the 
mean  motion  of  the  moon  in  her  orbit  exceeds  the  apparent 
motion  of  the  sun  by  about  12°  11'  in  a  day,  it  follows  that, 
about  four  days  after  the  new  moon,  she  will  be  seen  in  the 
evening  a  little  to  the  east  of  the  sun,  after  he  has  descended 
below  the  western  part  of  the  horizon.  A  spectator  will  see 
the  convex  part  of  the  moon  towards  the  west,  and  the  -horns 
or  cusps  towards  the  east :  or  if  the  observer  live  in  north 
latitude,  as  he  looks  at  the  moon  the  horns  will  appear  to  the 
left  hand ;  for  if  the  line  joining  the  cusps  of  the  moon  be 

What  truth  is  revealed  by  the  fact  that  the  same  face  of  th?  moon  is  al- 
ways towards  the  earth?  What  is  mean!  by  libration,  and  from  what  does 
it  arise  ?  How  do  we  know  that  the  moon  does  not  shine  by  its  own  light? 


148  ELEMENTARY  ASTRONOMY. 

bisected  by  a  perpendicular  passing  through  the  enlightened 
part  of  the  moon,  that  perpendicular  will  point  directly  to  the 
sun.  As  the  moon  continues  her  motion  eastward,  a  greater 
portion  of  her  surface  towards  the  earth  becomes  enlightened  ; 
and  when  she  is  90  degrees  eastward  of  the  sun,  which  will 
happen  about  7}  days  from  the  time  of  new  moon,  she  will 
come  to  the  meridian  about  six  o'clock  in  the  evening,  having 
the  appearance  of  a  bright  semi-circle.  Advancing  still  to  tiie 
eastward,  she  becomes  more  enlightened  towards  the  earth, 
and  at  the  end  of  about  14£  days,  she  will  come  to  the  meri- 
dian at  midnight,  being  diametrically  opposite  to  the  sun  ;  and 
consequently  she  appears  a  complete  circle,  and  it  is  said  to  be 
full  moon.  The  earth  is  now  between  the  sun  and  the  moon, 
and  that  half  of  her  surface,  which  is  constantly  turned  towards 
the  earth,  is  wholly  illuminated  by  the  direct  rays  of  the  sun , 
whilst  that  half  of  her  surface,  which  is  never  seen  from  the 
earth,  is  involved  in  darkness.  The  moon  continuing  her  pro- 
gress eastward,  she  becomes  deficient  on  her  western  edge,  and 
about  7-J  days  from  the  full  moon  she  is  again  within  90  degrees 
of  the  sun,  and  appears  a  semi-circle  with  the  convex  side 
turned  towards  the  sun:  moving  on  still  eastward,  the  deficiency 
on  her  western  edge  becomes  greater,  and  she  appears  a  cres- 
cent, with  the  convex  side  turned  towards  the  east,  and  her 
cusps  or  horns  turned  towards  the  west:  and  about  14^-  days 
from  the  full  moon  she  has  again  overtaken  the  sun,  this  period 
being  performed  in  29  days  12  hours  44  minutes  3  seconds,  at 
a  mean  rate,  as  has  been  mentioned  before.  Hence,  from  the 
new  moon  to  the  full  moon,  the  phases  are  horned,  half -moon, 
and  gibbous;  and  as  the  convex  or  well-defined  side  of  the  moon 
is  always  turned  towards  the  sun,  the  horns  or  irregular  side 
will  appear  to  the  east,  or  towards  the  left  hand  of  a  spectator 
in  north  latitude.  From  the  full  moon  to  the  change,  the  phases 

When  the  moon  is  full,  what  is  its  position  in  respect  to  the,  sun  ?  When 
the  moon  is  at  the  first  quarter,  what  is  its  position  in  respect  to  the  sun? 
When  at  the  last  quarter,  what  is  its  position,  and  about  what  time  would 
it  come  to  the  meridian  V 


LUNAR  APPEARANCES. 


149 


are  gibbous,  half-moon,  and  horned;  the  convex  or  well-defined 
side  of  her  face  will  appear  to  the  east,  and  her  horns  or  kregu- 
lar  side  towards  the  west,  or  to  the  right  hand  of  a  spectator. 

"  As  the  full  moons  always  happen  when  the  moon  is  directly 
opposite  to  the  sun,  all  the  full  moons,  in  our  winter,  happen 
when  the  moon  is  on  the  north  side  of  the  equinoctial.  The 
moon,  while  she  passes  from  Aries  to  Libra,  will  be  visible  at 
the  north  pole,  and  invisible  during  her  progress  from  Libra  to 
Aries  ;  consequently,  at  the  north  pole,  there  is  a  fortnight's 
moonlight  and  a  fortnight's  darkness  by  turns.  The  same 
phenomena  will  happen  at  the  south  pole  during  the  sun's  ab- 
sence in  our  summer." 

The  surface  of  the  moon  is  greatly  diversified  with  inequali- 


What  is  said  of  the  full  moons  in  winter  ? 
run  high,  or  low  ? 


Do  the  full  moons  of  suramei 


150          ELEMENTARY  ASTRONOMY. 

ties,  which,  through  a  telescope,  have  all  the  appearances  of 
hills,  mountains,  and  valleys.  Many  attempts  have  been  made, 
with  considerable  success,  to  delineate  the  face  of  the  moon  on 
paper,  as  it  appears  through  a  telescope,  and  the  figure  on  the 
preceding  page  is  a  copy  of  one  of  them. 

Dr.  Herschel  informs  us  that,  on  the  19th  of  April,  1787, 
lie  discovered  three  volcanoes  in  the  dark  pan  of  the  moon, 
two  of  them  apparently  extinct,  the  third  exhibited  an  actual 
eruption  "of  fire,  or  luminous  matter.  On  the  subsequent  night 
it  appeared  to  burn  with  greater  violence,  and  might  be  computed 
to  be  about  three  miles  in  diameter.  The  eruption  resembled 
a  piece  of  burning  charcoal,  covered  by  a  thin  coat  of  white 
ashes;  all  the  adjacent  parts  of  the  volcanic  mountain  were 
faintly  illuminated  by  the  eruption,  and  were  gradually  more 
obscure  at  a  greater  distance  from  the  crater.  That  the  surface 
of  the  moon  is  indented  with  mountains  and  caverns,  is  evident 
from  the  irregularity  of  that  part  of  her  surface  which  is  turned 
from  the  sun  :  for,  if  there  were  no  parts  of  the  moon  higher 
than  the  rest,  the  light  and  dark  parts  of  her  disc  at  the  time 
of  her  quadratures,  would  be  terminated  by  a  perfectly  Straight 
line ;  and  at  all  other  times  the  termination  would  be  an  ellip- 
tical line,  convex  towards  the  enlighted  part  of  the  moon,  in  the 
first  and  fourth  quarters,  and  concave  in  the  second  and  third: 
but  instead  of  these  lines  being  regular,  and  well  defined,  when 
the  moon  is  viewed  through  a  telescope,  they  appear  notched, 
and  broken  in  innumerable  places.  It  is  rather  singular  that 
the  edge  of  the  moon,  which  is  always  turned  towards  the  sun, 
is  regular  and  well  defined,  and  at  the  time  of  full  moon  no 
notches  or  indented  parts  are  seen  on  her  surface.  In  all  situ- 
ations of  the  moon,  the  elevated  parts  are  constantly  found  to 
cast  a  triangular  shadow  with  its  vertex  turned  from  the  sun  ; 
and,  on  the  contrary,  the  cavities  are  always  dark  on  the  side 
next  the  sun,  and  illuminated  on  the  opposite  side :  these  ap- 
pearances are  exactly  conformable  to  what  we  observe  of  hills 

How  long  are  the  winter  full  moons  visible  from  the  north  pole  ?  What 
full  moous  are  visible  more  than  24  hours,  as  seen  from  the  north  pole  ? 


LUNAR   ATMOSPHERE.  151 

and  valleys  on  the  earth :  and  even  in  the  dark  part  of  the  moon's 
disc,  near  the  borders  of  the  lucid  surface,  some  minute  specks 
have  been  seen,  apparently  enlightened  by  the  sun's  rays : 
these  shining  spots  are  supposed  to  be  the  summits  of  high 
mountains,  which  are  illuminated  by  the  sun,  while  the  ad- 
jacent valleys  nearer  the  enlightened  part  of  the  moon  are 
entirely  dark. 

Whether  the  moon  has  an  atmosphere  or  not,  is  a  question 
that  has  long  been  controverted  by  various  astronomers  ;  some 
endeavor  to  prove  that  the  moon  has  neither  an  atmosphere, 
seas,  nor  lakes ;  while  others  contend  that  she  has  all  these  in 
common  with  our  earth,  though  her  atmosphere  is  not  so  dense 
as  ours." 

Whenever  our  own  atmosphere  is  clear  and  transparent, 
every  appearance  of  hill,  and  valley  —  all  the  varieties  of  light, 
and  shade — indeed,  all  the  spots  on  the  moon  are  equally  well 
defined  and  distinct,  and  this  could  not  be,  were  the  moon  sur- 
rounded with  an  atmosphere  capable  of  holding  vapors,  and 
clouds,  like  the  atmosphere  of  our  earth.  Therefore,  most 
astronomers  conclude  that  such  an  atmosphere  does  not  there 
exist. 

On  the  other  hand,  we  must  not  forget  —  that  volcanoes  have 
been  observed  on  the  moon  —  and  we  can  have  no  distinct  idea 
of  combustion,  without  an  atmosphere  or  a  gas,  to  support  it. 
An  atmosphere  might  exist,  having  no  affinity  for  vapors,  one 
that  would  be  transparent,  and,  in  that  case  we  could  always 
see  through  it,  as  though  it  did  not  exist;  and  if  the  moon  has 
an  atmosphere,  it  must  be  one  of  that  kind. 

But  of  all  this,  nothing  is  positively  known. 

What  is  the  appearance  of  the  edge  of  themoori  between  the  illuminated 
and  unillurainated  parts  ?  What  does  this  appearance  surely  indicate  ? 
Why  have  astronomers  contended  that  the  moon  has  no  atmosphere  ?  Are 
you  sure  the  moon  has  no  atmosphere  ?  What  kind  of  an  atmosphere  may 
it  have  ? 


162  ELEMENTARY  ASTRONOMY. 

CHAPTER    II. 
ECLIPSES. 

THE  path  of  the  sun  through  the  heavens  is  the  same  every 
year.  It  is  the  ecliptic,  so  called,  because  all  eclipses  of  the 
sun,  and  moon,  take  place  when  the  moon  is  in  or  near  this  line. 

If  the  moon's  path  round  the  sphere  were  the  same  as  the 
sun's,  that  is,  if  the  moon  were  all  the  while  in  the  ecliptic, 
there  would  be  an  eclipse  of  the  sun  at  every  new  moon,  and 
an  eclipse  of  the  moon  at  every  full  moon.  The  moon's  orbit 
or  path,  as  we  have  seen  in  the  preceding  chapter,  intersects 
the  ecliptic  or  sun's  path  at  an  angle  of  5°  8';  the  points  of  in- 
tersection are  called  the  moon's  nodes ;  and  when  the  sun  is  in 
that  part  of  the  ecliptic  near  the  moon's  nodes,  the  moon  cannot 
pass  its  conjunction  with  the  sun  without  falling  in  range  be- 
tween some  part  of  the  ecliptic,  and  some  part  of  the  earth,  and 
that  produces  an  eclipse  of  the  sun.  The  two  nodes  are 
opposite  to  each  other,  and  when  the  sun  is  near  one  node,  the 
full  moon  will  take  place  when  the  moon  is  near  the  other  node ; 
and  the  sun,  earth,  and  moon  will  be  near  one  right  line  —  the 
earth  between  the  sun  and  moon  —  and  then  the  moon  must  fall 
into  some  portion  of  the  earth's  shadow,  and  this  produces  an 
eclipse  of  the  moon. 

If  the  moon's  nodes  were  always  at  the  same  points  on  the 
ecliptic,  eclipses  would  take  place  in  the  same  months  every  year, 
but  the  nodes  moving  backward  about  19°  19'  each  year,  the 
eclipses,  on  an  average,  come  about  19  days  earlier  each  suc- 
ceeding year.  Because  the  two  nodes  are  opposite  to  each 

Why  is  the  path  of  the  sun  among:  the  stars  called  the  ecliptic  ?  If  tho 
sun  and  moon  passed  round  the  earth  in  the  same  circle  or  path,  how  often 
would  eclipses  occur  ?  At  what  angle  does  the  moon's  path  intersect,  the 
ecliptic  ?  Where  must  the  sun  be  on  the  ecliptic  at  the  time  eclipses  oc«ur? 
If  the  moon's  nodes  were  stationary,  would  eclipses  then  occur  at  tho  ssuua 
seasons  of  the  year  continually  ? 


ECLIPTIC   LIMITS.  153 

other,  eclipses  must  happen  about  six  months  asunder.  For 
instance,  if  an  eclipse  occurs  in  the  month  of  March,  in  any 
year,  there  will  certainly  be  one  in  September,  or  on  some  of 
the  last  days  of  August,  at  the  new  or  full  moon.  If  an  eclipse 
occurs  in  June,  there  will  certainly  be  another  in  December. 
If  one  occurs  in  May  there  will  be  another  in  November,  and 
so  on  continually,  the  average  being  a  few  days  less  than  six 
months,  and  from  year  to  year,  the  average  time  being  at  in- 
tervals of  about  346  days. 

Whenever  the  moon  changes  within  17°  of  either  of  the 
moon's  nodes,  there  must  be  an  eclipse  of  the  sun.  That  is, 
the  sun  must  then  be  within  17°  of  one  of  the  nodes,  because 
at  the  time  of  change,  the  longitude  of  both  sun  and  moon  is 
then  the  same. 

Whenever  the  moon  fulls,  when  the  sun  is  within  12°  of 
either  node,  there  must  be  an  eclipse  of  the  moon. 

Hence,  the  number  of  eclipses  of  the  sun  which  take  place 
in  any  long  interval  of  time,  (say  19  years)  must  be  to  the 
number  of  eclipses  of  the  moon  as  17  to  12.  But,  an  eclipse 
of  the  sun  is  visible  from  only  a  very  small  portion  of  the  earth 
at  any  one  time,  while  an  eclipse  of  the  moon  is  visible  from  a 
whole  hemisphere  ;  hence  there  are  more  visible  eclipses  of  the 
moon  than  of  the  sun,  as  seen  from  any  one  place. 

The  least  number  of  eclipses  that  can  take  place  in  any  one 
year  is  two,  the  greatest  number  seven,  the  average  number  is 
four. 

When  but  two  eclipses  occur  in  a  year,  they  are  both  of  the 
sun,  and  are  central  as  seen  from  some  portion  of  the  earth 
near  the  plane  of  the  ecliptic.  That  is,  a  central  eclipse  would 
be  seen  from  some  latitude  near  the  sun's  declination.  For 
example  :  if  in  a  certain  year  there  were  but  two  eclipses,  both 

Why  do  eclipses  occur  at  opposite  months  of  the  year?  Give  the  limits 
within  which  the  sun  must  be  at  the  time  of  the  lunar  changes,  to  produce 
eclipses  ?  Give  the  ratio  between  the  number  of  eclipses  of  the  sim  and 
moon  that  take  place  in  any  long  interval  ?  State  the  least  and  greatest 
number  of  eclipses  that  can  take  place  in  any  one  year. 


164  ELEMENTARY  ASTRONOMY. 


would  be  of  the  sun,  and  suppose 
one  of  them  should  take  place  in 
June,  the  other  would  take  place 
in  December,  and  the  one  which 
took  place  in  June  would  be  cen- 
tral as  seen  from  some  latitude 
not  far  from  20°  north,  and  the  one 
in  December  would  be  central  as 
seen  from  some  latitude  not  far 
from  20°  south.  Eclipses  of  the 
sun  which  take  place  when  the 
sun  is  10  or  more  degrees  from 
the  node,  are  partial  eclipses,  visi- 
ble from  places  not  far  from  the 
poles  of  the  earth. 

To  show  more  clearly  that  the 
sun  and  moon  must  come  in  con- 
junction near  the  moon's  node, 
we  give  the  figure  in  the  margin. 

The  right  line  through  the  cen- 
ter represents  the  equator,  the 
curved  line  ^f'  ®  LOJ  the  ecliptic, 
and  the  other  curved  line  repre- 
sents the  moon's  path  crossing  the 
ecliptic  at  ^  and  £!>.  The  sun 
and  moon  are  represented  in  con- 
junction a  little  beyond  the  sign 
69,  but  the  two  paths  are  here  so  far 
asunder,  that  the  sun  and  moon 
cannot  come  in  range  with  each 
other  and  produce  an  eclipse.  It 
is  obviously  not  so,  on  the  paths 
near  their  intersections,  that  is, 
near  the  nodes. 

As  here  represented  the  as- 
cending node  is  in  longtitude 
about  210°,  and  the  descending 


ECLIPSES.  155 

node  is  in  longitude  about  30°,  and  this  was  the  position  of  the 
nodes  in  the  year  1846,  and  the  sun  is  at  these  points  of  the 
ecliptic  in  April  and  Octobej*,  and  therefore  the  eclipses  in  that 
year  must  have  been  and  really  were  in  those  months. 

To  make  a  general  and  rough  computation  of  the  times  that 
eclipses  will  occur,  all  we  have  to  do  is  to  get  the  position  of 
one  of  the  moon's  nodes,  by  observation  or  otherwise,  and 
then  trace  it  back  at  the  rate  of  19°  19'  for  365  days,  or  at  the 
rate  of  3'.  18  per  day. 

On  the  1st  of  January,  1850,  the  mean  longitude  of  the 
moon's  ascending  node  was  146°  7',  the  opposite  node  was 
therefore  in  longitude  326°.  The  sun  attains  the  longitude  of 
326°  on  or  about  the  15th  day  of  February  in  each  year,  and 
the  longitude  of  146°  on  or  about  the  19th  of  August.  There- 
fore the  new  and  full  moons  that  took  place  within  twelve  days 
of  these  times,  must  and  did  produce  eclipses. 

Diminishing  146°  7'  at  the  rate  of  19°  19'  for  each  365  days, 
brought  the  moon's  ascending  node  to  68°  47'. 8  on  the  1st  of 
January,  1854,  and  to  61°  23'  on  the  21st  of  May,  1854. 

The  sun  attains  this  longitude  on  the  22d  of  May,  and  on 
the  26th  of  May  the  moon  changed.  There  must  then  have  been 
an  eclipse.  The  sun  and  moon  at  that  time  were  about  4°  past 
the  moon's  ascending  node,  just  sufficient  to  cast  the  moon's 
shadow  into  the  northern  hemisphere,  making  a  central  eclipse 
at  noon,  in  latitude  45°  33'  north,  in  longitude  134°  45'  west. 

The  following  figure  may  assist  some  learners  to  form  a  dis- 
tinct and  general  idea  of  eclipses. 


How  far  does  the  node  run  back  in  365  days  ?  How  much  in  one  day  ? 
If  I  give  you  the  longitude  of  the  node,  can  you  tell  me  at  what  times  of 
the  year  eclipses  will  occur  ? 


156          ELEMENTARY  ASTRONOMY. 

When  an  observer  is  in  the  moon's  shadow,  the  dark  bod> 
of  the  moon  appears  to  him  on  the  face  of  the  sun.  When  an 
observer  on  the  earth  is  in  a  certain  space  adjoining  the 
shadow,  as  at  e  and  f,  a  part  of  the  sun  is  obscured  by  a  part 
of  the  moon.  When  the  moon  is  in  the  earth's  shadow,  it 
cannot  shine  because  the  direct  rays  of  the  sun  are  intercepted 
by  the  earth,  and  the  moon  is  said  to  be  in  an  eclipse.  Never- 
theless when  the  moon  is  near  the  center  of  the  earth's  shadow, 
a  sufficient  amount  of  light  is  refracted  through  the  earth's 
atmosphere  to  render  the  moon  darkly  visible. 

When  the  moon  is  eclipsed  to  the  inhabitants  of  the  earth, 
the  sun  must  be  eclipsed  to  an  observer  on  the  moon.  An  ob- 
server on  the  moon  will  see  the  sun  partially  eclipsed,  when 
the  moon  falls  into  the  partial  shadow  marked  P  P.  Although 
this  figure  answers  our  purpose  to  a  certain  extent,  it  also  illus- 
trates and  verifies  the  remarks  made  about  figures  on  page  142. 
The  distance  from  the  center  of  the  earth  to  the  moon's  orbit, 
is  30  diameters  of  the  earth,  but  in  the  figure  it  is  not  three 
diameters.  The  distance  to  the  sun  is  400  times  the  distance 
to  the  moon,  but  in  the  figure  it  is  not  five  times  that  distance. 
When  the  earth  is  made  of  any  apparent  magnitude,  there  is 
not  space  enough  on  any  paper  for  a  true  representation  of  any 
of  these  things. 

In  reality,  the  moon's  shadow  comes  to  a  point  at  about  the 
distance  of  the  earth  from  the  moon,  sometimes  before  it  ex- 
tends to  the  earth,  and  then  we  have  an  annular,  and  not  a 
total  eclipse. 

When  the  moon  is  near  her  perigee,  her  shadow  will  extend 
beyond  the  earth ;  when  near  her  apogee,  it  will  not  extend  to  the 
earth. 

As  we  have  before  seen,  the  mean  motion  of  the  moon 
exceeds  that  of  the  sun  by  such  an  amount  as  to  bring  the  two 

Can  the  moon  be  seen  when  in  a  total  eclipse  ?  Is  the  figure  on  page 
155  a  true  representation  of  the  distances  of  the  sun  and  moon  1  and  if  not, 
why  was  it  nqt  ma4e  so  ?  Is  the  moon's  shadow  always  of  the  same 
length  ?  and  if  nqt,  what  pauses  its  variation  1 


ECLIPSES.  157 

bodies  in  conjunction  or  opposition  at  the  average  interval  of 
29d.  12h.  44m.  3s.,  and  the  retrograde  motion  of  the  node  is 
such  as  to  bring  the  sun  to  the  same  node  at  intervals  of  346d. 
14h.  52m.  16s. 

Now  let  us  suppose  the  sun,  moon,  and  node  are  together  at 
any  point  of  time,  and  in  a  certain  unknown  interval  of  time, 
which  we  represent  by  P,  they  will  be  together  again.  In  this 
time  P,  we  will  suppose  the  moon  to  have  accomplished  m 
lunations,  and  the  sun  to  have  returned  to  the  same  node  n 
times. 

These  suppositions  give  the  following  equations  : 

(29d.  12A.  44m.)m=P.  (1) 

And  (346rf.  14A.  52m.)n=P.  (2) 

Neglecting  the  seconds  and  reducing  to  minutes,  we  have 

42524wi=P.  (3) 

499132ra=P.  (4) 

Dividing  (3)  by  (4),  and  reducing  the  numerator  and  de- 
nominator in  the  first  member,  gives  us 
10631m 


Or 

124783      m 

As  this  fraction  is  irreducible,  and  as  wand  n  must  be  whole 
numbers  to  answer  the  assumed  conditions,  therefore  the  smallest 
whole  number  for  m  is  124783,  and  for  n  10631. 

That  is,  we  see  by  equations  (1)  and  (2),  that  to  bring  the 
sun,  moon,  and  node  a  second  time  into  conjunction,  requires 
124783  lunations,  or  10631  returns  of  the  sun  to  the  node, 
which  is  10088  years,  and  about  197  days. 

We  say  about,  because  we  neglected  seconds  in  the  periods 
of  revolution,  and  because  the  mean  motions  will  change  in 
some  slight  degree  in  a  period  of  so  long  a  duration. 

What  number  of  lunations  are  required  for  the  sun,  moon,  and  node,  to 
come  in  the  .same  position  a  second  time  ?  Even  then,  will  the  coincidences 
be  exact? 


158          ELEMENTARY  ASTRONOMY. 

This  period,  however,  contemplates  an  exact  return  to  the 
same  positions  of  the  sun,  moon,  and  node,  so  that  a  line  drawn 
from  the  center  of  the  sun,  through  the  center  of  the  moon,  will 
strike  the  earth  at  the  same  distance  from  the  plane  of  the 
ecliptic ;  but  to  produce  an  eclipse,  it  is  not  necessary  that  an 
exact  return  to  former  positions  should  be  attained ;  a  greater  or 
less  approximation  to  former  circumstances  will  produce  a 
greater  or  less  approximation  to  a  former  eclipse  ;  but  exact 
coincidences,  in  all  particulars,  can  never  take  place,  however 
long  the  period. 

To  determine  the  time  when  a  return  of  eclipses  may  happen, 
(if  we  reckon  from  the  most  favorable  positions),  that  is,  com- 
mence with  the  supposition  that  the  sun,  moon,  and  node  are 
together,  it  is  sufficient  to  find  the  first  approximate  values  of 

4l     ,      ..         10631 

the  fraction   . 

124783 

If  we  find  the  successive  approximate  fractions,  by  the  rule 
of  continued  fractions  in  arithmetic,  we  shall  have  the  succes- 
sive periods  of  eclipses  which  will  happen  about  the  same 
node. 

The  approximate  fractions  are 

T'T         TV         33T         44y         Jft         rVVf 

These  fractions  show  that  at  1 1  lunations  from  the  time  an 
eclipse  occurs,  we  may  look  for  another;  but  if  not  at  11,  it 
must  be  at  12,  and  it  may  be  at  both  1 1  and  12  lunations. 

At  5  and  6  lunations  we  shall  find  eclipses  at  the  other  node. 
To  be  more  certain  when  an  eclipse  will  occur,  we  take  35 
lunations  from  a  preceding  eclipse,  which  is  1033  days  and  14 
hours  nearly.  There  was  a  total  eclipse  of  the  moon,  1851, 
July  12th,  19  hours.  Add  to  this  1033  days  14  hours,  will 
bring  up  to  May  12th,  1854,  the  time  of  another  lunar  eclipse. 

If  an  eclipse  occurs  within  10°  of  the  node,  it  is  certain  that 
an  eclipse  will  again  happen  at  the  lapse  of  47  lunations. 

The  period,  however,  which  is  most  known  and  most  remark  - 

What  do  the  numerators  of  the  series  of  fractions  indicate  on  page  158? 
What  do  the  denominators  indicate?  Lunations  between  what  events  ? 


ECLIPSES.  159 

able  appears  in  the  next  fraction,  which  shows  that  223  luna- 
tions have  a  very  close  approximate  value  to  19  revolutions  of 
the  sun  to  the  node. 

223  lunations  equal  -       6585.32  days. 

19  returns  of  Q  to  node  =6585.78  days. 

The  difference  is  but  a  fraction  of  a  day  ;  and  if  the  sun  and 
moon  were  at  the  node  in  the  first  instance,  they  would  be  only 
20'  from  the  node  at  the  expiration  of  the  period,  and  the  dif- 
ference in  the  moon's  latitude  less  than  2';  and,  therefore,  the 
eclipse  at  the  close  of  this  period  must  be  nearly  of  the  same 
magnitude  as  the  eclipse  at  the  beginning  ;  and  hence,  the 
expression  "a  return  of  the  eclipse,"  as  though  the  same  eclipse 
could  occur  twice. 

This  period  was  early  discovered  by  the  Chaldean  astrono- 
mers, and  hence,  it  is  sometimes  called  the  Chaldean  period, 
and  by  it  they  were  enabled  to  give  general  and  indefinite 
predictions  of  eclipses  that  were  to  happen ;  and  by  it  any 
learner,  however  crude  his  mathematical  knowledge,  can  desig- 
nate the  day  on  which  an  eclipse  will  occur,  from  simply  know- 
ing the  date  of  some  former  eclipse. 

The  period  of  6585  days  is  18  years  (including  four  leap 
years)  and  1 1  days  over. 

Therefore,  if  we  add  18  years  and  11  days  to  the  date  of 
some  former  eclipse,  we  shall  come  within  one  day  of  the  time 
of  an  eclipse  —  arid  it  will  be  an  eclipse  of  about  the  same  mag- 
nitude as  the  one  we  reckon  from. 

EX  AMP  LE  S. 

In  the  year  1806     16  June,  the  sun  was  eclipsed. 

Add  18     11 


1824     27  June,  the  sun  was  eclipsed. 
Add  18     10 


How  near  do  19  revoluiions  of  the  sun  to  the  node  correspond  to  223  lu- 
nations ?  What  is  meant  by  the  Chaldean  period  ?  What  is  its  length  and 
its  use?  An  eclipse  of  the  moon  occurred  July  1st,  1852  ;  when  may  we 
look  for  another  V 


160          ELEMENTARY  ASTRONOMY. 

1842       8  July,  the  sun  was  eclipsed. 

Add  18  10 

— — -  —  (In  this  period  are  5  leap  years.) 

1860  18  July,  the  sun  will  be  eclipsed. 

Add  18  11 

1878     29  July,  the  sun  will  be  eclipsed. 

And  thus  we  might  go  on  over  a  great  number  of  periods. 

The  present  year,  1854,  May  26,  a  very  remarkable  eclipse 
of  the  sun  will  appear  as  visible  in  the  north  eastern  part  of 
the  United  States.  From  this  we  can  predict  the  days  for  some 
future  eclipses,  as  follows : 

1854     26  May. 
Add  18     11 

1 872      6  June,  the  sun  will  be  eclipsed. 
Add  18     11 

1890     17  June,  the  sun  will  be  eclipsed. 

Thus  we  might  go  on,  forward  or  backward,  but  to  deter- 
mine on  what  portion  of  the  earth  any  future  eclipse  will  be 
visible,  we  must  compute  the  time  of  day  when  the  moon 
changes,  and  other  circumstances,  which  in  this  work  we  do 
not  pretend  to  take  into  account. 

These  periods  will  not  occur  continually,  because  the  returns 
are  not  exact,  and  the  small  variations  which  occur  at  each 
period,  will  gradually  wear  the  eclipse  away,  and  another 
eclipse  will  as  gradually  come  on  and  take  its  place. 

In  respect  to  these  periods,  those  eclipses  which  take  place 
about  the  moon's  ascending  node,  commence  near  the  north 
pole,  and  at  each  period  come  a  little  further  south,  and  finally 
leave  the  earth  at  the  south  pole,  after  the  lapse  of  96  periods, 
or  about  1729  years. 

Will  an  eclipse  occur  continually  at  periods  of  18  years  and  11  days  ? 
How  many  periods  are  required  to  work  one  of  these  periods  over  the  earth? 


ECLIPSES.  101 

Those  eclipses  which  take  place  about  the  moon's  descending 
node,  commence  near  the  south  pole  and  pass  over  the  earth  to 
the  northward,  in  the  same  interval  of  time. 

Eclipses  of  the  moon  arj  visible  at  all  places  where  the  moon 
is  above  the  horizon,  from  the  time  the  moon  enters  the  earth's 
shadow  until  it  leaves  it;  but  ellipses  of  the  sun  are  visible 
only  to  a  limited  distance  from  the  center  of  the  moon's  shadow, 
and  that  limit  does  not  exceed  60°  on  the  earth.  Eclipses  of 
the  sun,  which  occur  in  March,  pass  over  the  earth  in  a  north- 
easterly direction;  those  which  occur  in  September,  pass  over 
the  earth  in  a  southeasterly  direction  ;  and  those  which  occur 
in  June  and  December,  pass  over  in  nearly  an  eastern  direction. 

The  moon  eclipses  other  heavenly  bodies  as  well  as  the  sun. 
In  its  passage  through  the  heavens  the  moon  must  occasionally 
pass  between  us  and  the  planets,  and  between  us  and  all  those 
fixed  stars  that  are  situated  within  6°  of  the  ecliptic  on  either 
side.  For  in  the  period  of  18  years,  the  moon  must  some  time 
or  other  cover  each  portion  of  this  space  in  the  heavens. 

Such  eclipses  are  called  occupations,  and  if  we  include  all  the 
Btars  from  the  first  to  the  sixth  magnitude,  about  40  occultations 
take  place  each  month,  and  on  an  average  about  two  are  visible 
from  any  one  point  each  month.  Unless  it  be  an  occasional 
eclipse  of  some  of  the  larger  planets  by  the  moon,  occultations 
are  not  visible  to  the  naked  eye,  as  the  light  of  the  moon 
obscures  that  of  the  stars,  when  the  moon  is  near  them,  and 
therefore  none  but  astronomers  who  have  telescopes,  can  ob- 
serve these  eclipses,  and  no  others  seem  to  be  aware  of  their 
existence. 

A  list  of  occultations  can  be  found  each  year  in  the  English 
Nautical  Almanac. 

In  what  direction  do  solar  eclipses  pass  over  the  earth  ?  Does  the  moon 
eclipse  other  bodies  than  the  sun  ?  What  are  occultations,  and  about  ho\v 
many  occur  each  month  ? 

14 


162  ELEMENTARY  ASTRONOMY. 

CHAPTER    III. 
THE  TIDES. 

THE  alternate  rise  and  fall  of  the  surface  of  the  sea,  as  ob- 
served at  all  places  directly  connected  with  the  waters  of  the 
ocean,  is  called  tide  ;  and  before  its  cause  was  definitely  known, 
it  was  recognized  as  having  some  hidden  and  mysterious  connec- 
tion with  the  moon,  for  it  rose  and  fell  twice  in  every  lunar  day. 
High  water  and  low  water  had  no  connection  with  the  hour  of 
the  day,  but  it  always  occurred  in  about  such  an  interval  of  time 
after  the  moon  had  passed  the  meridian. 

When  the  sun  and  moon  were  in  conjunction,  or  in  opposition, 
the  tides  were  observed  to  be  higher  than  usual. 

When  the  moon  was  nearest  the  earth,  in  her  perigee,  other 
circumstances  being  equal,  the  tides  were  observed  to  be  higher 
than  when,  under  the  same  circumstances,  the  moon  was  in  her 
apogee. 

The  space  of  time  from  one  tide  to  another,  or  from  high 
water  to  high  water  (when  undisturbed  by  wind),  is  12  hours 
and  about  24  minutes,  thus  making  two  tides  in  one  lunar  day ; 
showing  high  water  on  opposite  sides  of  the  earth  at  the  same 
time. 

The  declination  of  the  moon,  also,  has  a  very  sensible  influ- 
ence on  the  tides.  When  the  declination  is  high  in  the  north, 
the  tide  in  the  northern  hemisphere,  which  is  next  to  the  moon, 
is  greater  than  the'  opposite  tide  ;  and  when  the  declination  of 
the  moon  is  south,  the  tide  opposite  to  the  moon  is  greatest 

It  is  considered  mysterious,  by  most  persons,*  that  the  moon 

Give  a  definition  of  tides.  What  connection  was  observed,  in  early 
times,  between  the  moon  and  times  of  high  water?  When  were  tides 
higher  than  usual?  What  is  the  time  from  one  high  tide  to  another? 


THE   TIDES.  163 

by  its  attraction  should  be  able  to  raise  a  tide  on  the  opposite 
side  of  the  earth. 

That  the  moon  should  attract  the  water  on  the  side  of  the 
earth  next  to  her,  and  thereby  raise  a  tide,  seems  rational  and 
natural,  but  that  the  same  simple  action  also  raises  the  oppo- 
site tide,  is  not  as  readily  admitted;  and,  in  the  absence  of  clear 
illustration,  it  has  often  excited  mental  rebellion — and  not  a 
few  popular  lecturers  have  attempted  explanations  from  false 
and  inadequate  causes. 

But  the  true  cause  is  the  sun  and  moon's  attraction  ;  and 
until  this  is  clearly  and  decidedly 
understood — not  merely  assented 
to,  but  fully  comprehended  —  it  is 
impossible  to  understand  the  com- 
mon results  of  the  theory  of  gravity, 
which  are  constantly  exemplified  in 
the  solar  system. 

We  now  give  a  rude,  but  striking, 
and  we  hope,  a  satisfactory  expla- 
nation. 

Conceive  the  frame -work  of  the 
earth  to  be  an  inflexible  solid,  as  it 
really  is,  composed  of  rock,  and  in- 
capable of  changing  its  form  under 
any  degree  of  attraction  ;  conceive 
also  that  this  solid  protuberates  out 
of  the  sea,  at  opposite  points  of  the 
earth,  at  A  and  B,  as  represented 
in  the  figure,  A  being  on  the  side  of 
the  earth  next  to  the  moon,  m,  and 
B  opposite  to  it.  Now,  in  connec- 
tion with  this  solid,  conceive  a  great 
portion  of  the  earth  to  be  composed 

What  is  the  true  course  of  the  tides  ?    Explain  the  true  cause  of  the  tide 
rising  on  the  side  of  the  earth  opposite  the  moon  ? 


164  ELEMENTARY  ASTRONOMY. 

of  water,  whose  particles  are  inert,  but  readily  move  among 
themselves. 

The  solid  AB  cannot  expand  under  the  moon's  attraction, 
and  if  it  move,  the  whole  mass  moves  together,  in  virtue  of 
the  moon's  attraction  on  its  center  of  gravity.  But  the  particles 
of  water  at  a,  being  free  to  move,  and  being  under  a  more 
powerful  attraction  than  the  center  of  the  solid,  rise  toward  A, 
producing  a  tide. 

The  particles  of  water  at  I  being  less  attracted  toward  m  than 
the  center  of  the  solid,  will  not  move  toward  m  as  fast  as  the 
solid,  and  being  inert,  they  will  be,  as  it  were,  left  behind.  The 
solid  is  drawn  toward  the  moon  more  powerfully  than  the  parti- 
cles of  water  at  b,  and  the  solid  sinks  in  part  into  the  water, 
but  the  observer  at  B,  of  course,  conceives  it  the  water  rising 
upon  the  shore  (which  in  effect  it  is),  thereby  producing  a  tide. 

Mathematicians  have  found,  by  analytical  investigation,  that 
the  power  of  the  moon's  attraction  to  produce  the  tides,  varies 
as  the  inverse  cube  of  the  distance  to  the  moon. 

The  sun's  attraction  on  the  earth  is  vastly  greater  than  that 
of  the  moon ;  but  by  reason  of  the  great  distance  to  the  sun, 
that  body  attracts  every  part  of  the  earth  nearly  alike,  and, 
therefore,  it  has  much  less  influence  in  raising  a  tide  than  the 
moon. 

From  a  long  course  of  observations  made  at  Brest,  in  France, 
it  has  been  decided  that  the  medium  high  tides,  when  the  sun 
and  moon  act  together  in  the  syzigies,  is  19. 317  feet;  and 
when  they  act  against  each  other  (the  moon  in  quadrature), 
the  tides  are  only  9.151  feet.  Hence  the  efficacy  of  the  moon, 
in  producing  the  tides,  is  to  that  of  the  sun,  as  the  number 
14.23  to  5.08.* 

*  These  numbers  are  found  as  follows  :  Let  m  represent  the  effective 
force  of  the  moon,  and  s  that  of  the  sun. 

Then    m-f-?=]9.3l7,     and     m—s    9.151. 
Whence     T?i=l4.23,     and     «=5.08. 

Is  the  sun's  attraction  on  the  earth  greater  than  that  of  the  moon  ?  If 
so,  why  do  we  not  have  greater  tides  from  the  action  of  the  sun  than  from 
the  action  of  the  mooii  ? 


THE   TIDES.  165 

Among  the  islands  in  the  Paciiic  ocean,  observations  give 
the  proportion  of  5  to  2.2,  for  the  relative  influences  of  these 
two  bodies;  and,  as  this  locality  is  more  favorable  to  accuracy 
than  that  of  Brest,  it  is  he  proportion  generally  taken. 

Having  the  relative  influences  of  two  bodies  in  raising  the 
tides,  we  have  the  relative  masses  of  those  two  bodies,  pro- 
vided they  were  at  the  same  distance.  But  the  influence  of 
the  moon  on  the  tides  lias  a  variation  corresponding  with  the 
inverse  cube  of  the  distance,  and  the  distance  to  the  sun  is 
397.2  times  the  mean  distance  to  the  moon.  Hence,  to  have 
the  influence  of  the  moon  on  the  tides,  when  that  body  is 
removed  to  the  distance  of  the  sun,  we  must  divide  its  ob- 
served influence  by  the  cube  of  397.2.  That  is,  the  mass  of 

the  nioon,  is  to  the  mass  of  the  sun,  as  the  number  — - 

is  to  the  number  2.2. 

If  the  mass  of  the  earth  is  assumed  to  be  unity,  the  mass 
of  the  sun,  is  found  by  its  attraction,  to  be  354945;  and  now 
if  we  represent  the  mass  of  the  moon  by  m,  we  shall  have  the 
following  proportion : 

m  :  354945  :  : :  2.2. 

(397.2)3 

This  proportion  makes  m,  the  mass  of  the  moon,  to  be  nearly 
T'T.  The  more  correct  value  is  ^j,  computed  from  other  and 
more  reliable  data,  which  is  to  be  found  in  our  larger  work. 

The  time  of  high  water  at  any  given  point  is  not  commonly 
at  the  time  the  moon  is  on  the  meridian,  but  two  or  three  hours 
after,  owing  to  the  inertia  of  the  water ;  and  places,  not  far 
from  each  other,  have  high  water  at  very  different  times  on  the 
same  day,  according  to  the  distance  and  direction  that  the  tide 
wave  has  to  undulate  from  the  main  ocean. 

The  interval  between  the  meridian  passage  of  the  moon  and 
the  time  of  high  water,  is  nearly  constant  at  the  same  place. 
It  is  about  fifteen  minutes  less  at  the  syzigies  than  at  the  quad- 
Is  the  time  of  high  water  when  the  moon  is  on  the  meridian  ? 


166          ELEMENTARY  ASTRONOMY. 

ratures ;  but  whatever  the  mean  interval  is  at  any  place,  it  is 
called  the  establishment  of  the  port. 

It  is  high  water  at  Hudson,  on  the  Hudson  river,  before  it  is 
high  water  at  New  York,  on  the  same  day;  but  the  tide  wave 
that  makes  high  water  one  day  at  Hudson,  made  high  water  at 
New  York  the  day  before  ;  and  the  tide  waves  that  make  high 
water  now,  were,  probably,  raised  in  the  ocean  several  days 
ago ;  and  the  tides  would  not  instantly  cease  on  the  annihilation 
of  the  sun  and  moon. 

The  actual  rise  of  the  tide  is  very  different  in  different  places, 
being  greatly  influenced  by  local  circumstances,  such  as  the 
distance  and  direction  to  the  main  ocean,  the  shape  and  depth 
of  the  bay  or  river,  <fec.  <fcc. 

In  the  Bay  of  Fundy  the  tide  is  sometimes  fifty  and  sixty 
feet ;  in  the  Pacific  ocean,  it  is  about  two  feet ;  and  in  some 
places  in  the  West  Indies,  it  is  scarcely  fifteen  inches.  In  in- 
land seas  and  lakes  there  are  no  tides,  because  the  moon's  attrac- 
tion is  equal,  or  nearly  so,  over  their  whole  extent  of  surface. 

The  following  table  shows  the  hight  of  the  tides  at  the  most 
important  points  along  the  coast  of  the  United  States,  as  ascer- 
tained by  recent  observation : 

Feet. 

Annapolis,  (Bay  of  Fundy), 60 

Apple  River, 50 

Chicneito  Bay,  (north  part  of  the  Bay  of  Fundy,).   60 

Passamaquoddy  River, 25 

Penobscot  River, 10 

Boston, 11 

Providence,  R.  I., 5 

New  Bedford, 5 

New  Haven, 8 

New  York, 5 

Cape  May, 6 

Cape  Henry, 4^- 

Why  do  we  have  no  tides  on  inland  seas  and  lakes  ?  What  is  meant  by 
the  establishment  of  the  port  ? 


COMETS.  1C7 

CHAPTER   IV. 

ON   COMETS. 

BESIDES  the  planets,  and  their  satellites,  there  are  great 
numbers  of  other  bodies,  which  gradually  come  into  view, 
increasing  in  brightness  and  velocity,  until  they  attain  a  max- 
imum, and  then,  as  gradually  diminish,  pass  off,  and  are  lost 
in  the  distance. 

"  These  bodies  are  comets.  From  their  singular  and  unusual 
appearance,  they  were  for  a  long  time  objects  of  terror  to  man- 
kind, and  were  regarded  as  harbingers  of  some  great  calamity. 

"  The  luminous  train  which  accompanied  them  was  particu- 
larly alarming,  and  the  more  so  in  proportion  to  its  length.  It 
is  but  little  more  than  half  a  century  since  these  superstitious 
fears  were  dissipated  by  a  sound  philosophy  ;  and  comets, 
being  now  better  understood,  excite  only  the  curiosity  of 
astronomers  and  of  mankind  in  general.  These  discoveries, 
which  give  fortitude  to  the  human  mind,  are  not  among  the 
least  useful. 

"It  was  formerly  doubted  whether  comets  belonged  to  the 
class  of  heavenly  bodies,  or  were  only  meteors  engendered  for- 
tuitously in  the  air,  by  the  inflammation  of  certain  vapors. 
Before  the  invention  of  the  telescope,  there  were  no  means  of 
observing  the  progressive  increase  and  diminution  of  their 
light.  They  were  seen  but  for  a  short  time,  and  their  appear- 
ance and  disappearance  took  place  suddenly.  Their  light  and 
vapory  tails,  through  which  the  stars  were  visible,  and  their 
whiteness  often  intense,  seemed  to  give  them  a  strong  resem- 

What  is  the  general  appearance  of  a  comet  ?  Like  the  planets,  are  they 
observed  to  traverse  the  whole  circumference  of  the  heavens,  or  do  they 
appear  only  for  a  season,  in  limited  spaces  ? 


108          ELEMENTARY  ASTRONOMY. 

biance  to  those  transient  fires,  which  we  call  shooting  stars 
Apparently,  they  differed  from  these  only  in  duration.  They 
might  be  only  composed  of  a  more  compact  substance  capable 
of  retarding  for  a  longer  time  their  dissolution.  But  these 
opinions  are  no  longer  maintained ;  more  accurate  observations 
have  led  to  a  different  theory. 

"  All  the  comets  hitherto  observed  have  a  small  parallax, 
which  places  them  far  beyond  the  orbit  of  the  moon  ;  they  are 
not,  therefore,  formed  in  our  atmosphere.  Moreover,  their  ap- 
parent motion  among  the  stars  is  subject  to  regular  laws,  which 
enable  us  to  predict  their  whole  course  from  a  small  number  of 
observations.  This  regularity  and  constancy  evidently  indicate 
durable  bodies  ;  and  it  is  natural  to  conclude  that  comets  are 
as  permanent  as  the  planets,  but  subject  to  a  different  kind  of 
movement. 

"  When  we  observe  these  bodies  with  a  telescope,  they  re- 
semble a  mass  of  vapor,  at  the  center  of  which  is  commonly 
seen  a  nucleus,  more  or  less  distinctly  terminated.  Some, 
however,  have  appeared  to  consist  of  merely  a  light  vapor, 
without  a  sensible  nucleus,  since  the  stars  are  visible  through 
it.  During  their  revolution,  they  experience  progressive  varia- 
tions in  their  brightness,  which  appear  to  depend  upon  their 
distance  from  the  sun,  either  because  the  sun  inflames  them 
by  its  heat,  or  simply  on  account  of  a  stronger  illumination. 
When  their  brightness  is  greatest,  we  may  conclude  from  this 
very  circumstance  that  they  are  near  their  perihelion.  Their 
light  is  at  first  very  feeble,  but  becomes  gradually  more  vivid, 
until  it  sometimes  surpasses  that  of  the  brightest  planets  ;  after 
which  it  declines  by  the  same  degrees  until  it  becomes  imper- 
ceptible. We  are  hence  led  to  the  conclusion  that  comets, 
coming  from  the  remote  regions  of  the  heavens,  approach,  in 
many  instances,  much  nearer  the  sun  than  the  planets,  and 
then  recede  to  much  greater  distances." 

How  is  it  known  that  some  comets  are  merely  vapor  ?     Do  comets  in- 
crease and  decrease  in  real  brightness  ? 


COMETS.  169 

The  following  figure  we  give  to  illustrate  the  foregoing  de- 
scription. 


"Since  comets  are  bodies  which  seem  to  belong  to  our 
planetary  system,  it  is  natural  to  suppose  that  they  move  about 
the  sun  like  planets,  but  in  orbits  extremely  elongated.  These 
orbits  must,  therefore,  still  be  ellipses,  having  their  foci  at  the 
center  of  the  sun,  but  having  their  major  axes  almost  infinite, 
especially  with  respect  to  us,  who  observe  only  a  small  portion 
of  the  orbit,  namely,  that  in  which  the  comet  becomes  visible 
as  it  approaches  the  sun.  Accordingly,  the  orbits  of  comets 
must  take  the  form  of  a  parabola,  for  we  thus  designate  the 
curve  into  which  the  ellipse  passes,  when  indefinitely  elongated. 

"About  120  comets  have  been  calculated  upon  the  theory 
of  the  parabolic  motion,  and  the  observed  places  are  found  to 
answer  to  such  a  supposition.  We  can  have  no  doubt,  there- 
fore, that  this  is  conformable  to  the  law  of  nature.  We  have 
thus  obtained  precise  knowledge  of  the  motions  of  these  bodies, 
and  are  enabled  to  follow  them  in  space.  This  discovery  has 
given  additional  confirmation  to  the  laws  of  Kepler,  and  led  to 
several  other  important  results. 

Are  the  orbits  of  the  comets  elliptical  or  parabolic  ?  If  not  parabolic, 
why  are  computations  made  on  that  hypothesis  ?  Do  the  comets  all  move 
in  the  same  direction  as  the  planets  ? 

15 


HO          ELEMENTARY  ASTRONOMY. 

"  Comets  do  not  all  move  from  west  to  east  like  the  planets, 
Some  have  a  direct,  and  some  a  retrograde  motion. 

"  Their  orbits  are  not  comprehended  within  a  narrow  zone 
of  the  heavens,  like  those  of  the  principal  planets.  They  vary 
through  all  degrees  of  inclination.  There  are  some  whose 
planes  nearly  coincide  with  that  of  the  ecliptic,  and  others  have 
their  planes  nearly  perpendicular  to  it. 

"  It  is  farther  to  be  observed  that  the  tails  of  comets  begin  to 
appear,  as  the  bodies  approach  near  the  sun  ;  their  length  in- 
creases with  this  proximity,  and  they  do  not  acquire  their 
greatest  extent,  until  after  passing  the  perihelion.  The  direc- 
tion is  generally  opposite  to  the  sun,  forming  a  curve  slightly 
concave,  the  sun  on  the  concave  side. 

"  The  portion  of  the  comet  nearest  to  the  sun  must  move 
more  rapidly  than  its  remoter  parts,  and  this  will  account  for 
the  lengthening  of  the  tail. 

"  The  tail,  however,  is  by  no  means  an  invariable  appendage 
of  comets.  Many  of  the  brightest  have  been  observed  to  have 
short  and  feeble  tails,  and  not  a  few  have  been  entirely  without 
them.  Those  of  1585  and  1763  oifered  no  .vestige  of  a  tail; 
and  Cassini  describes  the  comet  of  1682  as  being  as  round  and 
as  bright  as  Jupiter.  On  the  other  hand,  instances  are  not 
wanting  of  comets  furnished  with  many  tails,  or  streams  of 
diverging  light.  That  of  1744  had  no  less  than  six,  spread 
out  like  an  immense  fan,  extending  to  a  distance  of  nearly  30 
degrees  in  length. 

"  The  smaller  comets,  such  as  are  visible  only  in  telescopeo, 
or  with  difficulty  by  the  naked  eye,  and  which  are  by  far  the 
most  numerous,  offer  very  frequently  no  appearance  of  a  tail, 
and  appear  only  as  round  or  somewhat  oval  vaporous  masses, 
more  dense  toward  the  center ;  where,  however,  they  appear  to 
have  no  distinct  nucleus,  or  any  thing  which  seems  entitled  to 
be  considered  as  a  solid  body. 

"The  tail  of  the  comet  of  1456  was  60  degrees  long.     That 

Mention  the  apparent  lengths  of  the  tails  of  some  of  the  comets  ?  J>o 
•ny  of  the  comets  have  wore  than  one  tail  ? 


COMETS.  171 

of  1618,  100  degrees,  so  that  its  tail  had  not  all  risen  when  its 
head  reached  the  middle  of  the  heavens.  The  comet  of  1680 
was  so  great,  that  though  its  head  set  soon  after  the  sun,  its 
tail,  70  degrees  long,  continued  visible  all  night.  The  comet  of 
1689  had  a  tail  68  degrees  long.  That  of  1769  had  a  tail  more 
than  90  degrees  in  length.  That  of  1.81 1  had  a  tail  23  degrees 
long.  The  recent  comet  of  1843  had  a  tail  60  degrees  in  length. 

"  When  we  have  determined  the  elements  of  a  comet's  orbit, 
we  compare  them  with  those  of  comets  before  observed,  and 
see  whether  there  is  an  agreement  with  respect  to  any  of  them. 
If  there  is  a  perfect  identity  as  to  the  elements,  we  should  have 
no  hesitation  in  concluding  that  they  belonged  to  different  ap- 
pearances of  the  same  comet.  But  this  condition  is  not  rigor- 
ously necessary ;  for  the  elements  of  the  orbit  may,  like  those 
of  other  heavenly  bodies,  have  undergone  changes  from  the 
perturbations  of  the  planets,  or  from  their  mutual  attractions. 
Consequently,  we  have  only  to  see  whether  the  actual  elements 
are  nearly  the  same  with  those  of  any  comet  before  observed, 
and  then,  by  the  doctrine  of  chances,  we  can  judge  what  re- 
liance is  to  be  placed  upon  this  resemblance. 

"Dr.  Halley  remarked  that  the  comets  observed  in  1531, 
1607,  1682,  had  nearly  the  same  elements ;  and  he  hence  con- 
cluded that  they  belonged  to  the  same  comet,  which,  in  151 
years,  made  two  revolutions,  its  period  being  about  76  years. 
It  actually  appeared  in  1759,  agreeably  to  the  prediction  of 
this  great  astronomer  ;  and  again  in  1 835,  by  the  computation 
of  several  eminent  astronomers.  According  to  Kepler's  third 
law,  if  we  take  for  unity  half  the  major  axis  of  the  earth's 
orbit,  the  mean  distance  of  this  comet  must  be  equal  to  the 
cube  root  of  the  square  of  76,  that  is,  to  17.95.  The  major 
axis  of  its  orbit  must,  therefore,  be  35.9  ;  and  as  its  observed 
perihelion  distance  is  found  to  be  0.58,  it  follows  that  its  aphe- 
lion distance  is  equal  to  35.32.  It  departs,  therefore,  from  the 
sun  tc  thirty-five  times  the  distance  of  the  earth,  and  after- 

From  what  data  do  astronomers  predict  the  return  of  comets  ? 


172          ELEMENTARY  ASTRONOMY. 

ward  approaches  nearly  twice  as  near  the  sun  as  the  earth  is, 
thus  describing  an  ellipse  extremely  elongated. 

"  The  intervals  of  its  return  to  its  perihelion  are  not  con* 
etantly  the  same.  That  between  1531  and  1607  was  three 
months  longer  than  that  between  1607  and  1682;  and  this 
last  was  18  months  shorter  than  the  one  between  1682  and 
1759.  It  appears,  therefore,  that  the  motions  of  comets  are 
subject  to  perturbations,  like  those  of  the  planets,  and  to  a 
much  more  sensible  degree. 

"  Comets,  in  passing  among  and  near  the  planets,  are  mate- 
rially drawn  aside  from  their  courses,  and  in  some  cases,  have 
their  orbits  entirely  changed.  This  is  remarkably  the  case 
with  Jupiter,  which  seems,  by  some  strange  fatality,  to  be 
constantly  in  their  way,  and  to  serve  as  a  perpetual  stumbling- 
block  to  them.  In  the  case  of  the  remarkable  comet  of  1770, 
which  was  found  by  Lexell  to  revolve  in  a  moderate  ellipse  in 
the  period  of  about  five  years,  and  whose  return  was  predicted 
by  him  accordingly,  the  prediction  was  disappointed  by  the 
comet  actually  getting  entangled  among  the  satellites  of  Jupiter, 
and  being  completely  thrown  out  of  its  orbit  by  the  attraction 
of  that  planet,  and  forced  into  a  much  larger  ellipse.  By  this 
extraordinary  renconter,  the  motions  of  the  satellites  suffered  not 
the  least  perceptible  derangement — a  sufficient  proof  of  the  small- 
ness  of  the  comet's  mass." 

The  comet  of  1456,  represented  as  having  a  tail  of  60°  in 
length,  is  now  found  to  be  Halley's  comet,  which  has  made 
several  returns  —  in  1531,  1607,  1682,  1759,  and  recently,  in 
1835.  In  1607  the  tail  was  said  to  have  been  over  30  degrees 
in  length;  but  in  1835  the  tail  did  not  exceed  20  degrees. 
Does  it  lose  substance,  or  does  the  matter  composing  the  tail 
condense  ?  or,  have  we  received  only  exaggerated  and  dis- 
torted accounts  from  the  earlier  times,  such  as  fear,  superstition, 
and  awe,  always  put  forth?  We  ask  these  questions,  but  can- 
not answer  them. 

Does  the  same  comet  return  at  equal  intervals?  and  if  not,  why?  What 
circumstances  show  us  that  cornets  have  small  masses  ? 


COMETS. 


173 


"  Professor  Kendall,  in  his  Uranography,  speaking  of  the 
fears  occasioned  by  comets,  says  :  Another  source  of  appre- 
hension, with  regard  to  comets,  arises  from  the  possibility  of 
their  striking  our  earth.  It  is  quite  probable  that  even  in  the 
historical  period,  the  earth  has  been  enveloped  in  the  tail  of  a 
comet.  It  is  not  likely  that  the  effect  would  be  sensible  at  the 
time.  The  actual  shock  of  the  head  of  a  comet  against  the 
earth  is  extremely  improbable.  It  is  not  likely  to  happen  once 
in  a  million  of  years. 

11  If  such  a  shock  should  occur,  the  consequences  might 
perhaps  be  very  trivial.  It  is  quite  possible  that  many  of  the 
comets  are  not  heavier  than  a  single  mountain  on  the  surface 
of  the  earth.  It  is  well  known  that  the  size  of  mountains  on 
the  earth  is  illustrated  by  comparing  them  to  particles  of  dust 
on  a  common  globe." 

The  following  cut  represents  a  telescopic  view  of  the  comet 
of  1811: 


Is  there  a  possibility  that  a  comet  may  strike  the  earth  ?    If  such  a  thing 
should  occur,  would  it  cause  the  destruction  of  the  earth  ? 


174          ELEMENTARY  ASTRONOMY. 

CHAPTER    Y. 
ON  THE  PECULIARITIES  OF   THE  FIXED  STARS. 

FOR  the  facts  as  contained  in  the  subject  matter  of  this 
chapter,  we  must  depend  wholly  on  authority  ;  for  that  reason 
we  give  only  a  compilation,  made  in  as  brief  a  manner  as  the 
nature  of  the  subject  will  admit. 

In  the  first  part  of  this  work  it  was  soon  discovered  that  the 
fixed  stars  were  more  remote  than  the  sun  or  planets  ;  and  now, 
having  determined  their  distances,  we  may  make  further  in- 
quiries as  to  the  distances  to  the  stars,  which  will  give  some 
index  by  which  to  judge  of  their  magnitudes,  nature,  and 
peculiarities. 

"  It  would  be  idle  to  inquire  whether  the  fixed  stars  have  a 
sensible  parallax,  when  observed  from  different  parts  of  the 
earth.  We  have  already  had  abundant  evidence  that  their  dis- 
tance is  almost  infinite.  It  is  only  by  taking  the  longest  base 
accessible  to  us,  that  we  can  hope  to  arrive  at  any  satisfactory 
result. 

"Accordingly,  we  employ  the  major  axis  of  the  earth's  orbit, 
which  is  nearly  200  millions  of  miles  in  extent.  By  observing 
a  star  from  the  two  extremities  of  this  orbit,  at  intervals  of  six 
months,  and  applying  a  correction  for  all  the  small  inequalities, 
the  effect  of  which  we  have  calculated,  we  shall  know  whether 
the  longitude  and  latitude  are  the  same  or  not  at  these  two 
epochs. 

"  It  is  obvious,  indeed,  that  the  star  must  appear  more  ele- 
vated above  the  plane  of  the  ecliptic  when  the  earth  is  in  the 
part  of  its  orbit  which  is  nearest  to  the  star,  and  more  de- 
pressed when  the  contrary  takes  place.  The  visual  rays  drawn 

What  base  is  taken  to  measure  the  distance  to  the  fixed  stars?  Do  the 
fixed  stars  appear  in  the  same  direction  from  each  extremity  of  this  base? 
And  if  so,  what  does  that  prove? 


PECULIARITIES  OF  THE  FIXED  STARS.  175 

from  the  earth  to  the  star,  in  these  two  positions,  differ  from 
the  straight  line  drawn  from  the  star  to  the  center  of  the  earth's 
orbit ;  and  the  angle  which  either  of  them  forms  with  this 
straight  line,  is  called  the  annual  parallax. 

"  As  the  earth  does  not  pass  suddenly  from  one  point  of  its 
orbit  to  the  opposite,  but  proceeds  gradually,  if  we  observe  the 
positions  of  a  star  at  the  intermediate  epochs,  we  ought,  if  the 
annual  parallax  is  sensible,  to  see  its  effects  developed  in  the 
same  gradual  manner.  For  example,  if  the  star  is  placed  at 
the  pole  of  the  ecliptic,  the  visual  rays  drawn  from  it  to  the 
earth,  will  form  a  conical  surface,  having  its  apex  at  the  star, 
and  for  its  base,  the  earth's  orbit.  This  conical  surface  being 
produced  beyond  the  star,  will  form  another  opposite  to  the 
first,  and  the  intersection  of  this  last  with  the  celestial  sphere, 
will  constitute  a  small  ellipse,  in  which  the  star  will  always 
appear  diametrically  opposite  to  the  earth,  and  in  the  prolonga- 
tion of  the  visual  rays  drawn  to  the  apex  of  the  cones. 

"  But  notwithstanding  all  the  pains  that  have  been  taken  to 
multiply  observations,  and  all  the  care  that  has  been  used  to 
render  them  perfectly  exact,  we  have  been  able  to  discover 
nothing  which  indicates,  with  certainty,  even  the  existence  of 
an  annual  parallax,  to  say  nothing  of  its  magnitude.  Yet  the 
precision  of  modern  observations  is  such,  that  if  this  parallax 
were  only  1",  it  is  altogether  probable  that  it  would  not  have 
escaped  the  multiplied  efforts  of  observers,  and  especially  those 
of  Dr.  Bradley,  who  made  many  observations  to  discover  it, 
and  who,  in  this  undertaking,  fell  unexpectedly  upon  the  phe- 
nomena of  aberration*  and  nutation.  These  admirable  dis- 
coveries have  themselves  served  to  show,  by  the  perfect  agree- 
ment which  is  thus  found  to  take  place  among  observations, 
that  it  is  hardly  to  be  supposed  that  the  annual  parallax  can 
amount  to  I".  The  numerous  observations  on  the  polar  star, 
employed  in  measuring  an  arc  of  the  meridian,  through  France, 

*  Subjects  which  will  come  in  tiie  next  chapter. 

What  is  meant  by  annual  parallax  ?    Has  such  a  parallax  been  observed? 
And  if  not,  why? 


176          ELEMENTARY  ASTRONOMY. 

have  been  attended  with  a  similar  result,  as  to  the  amount  of 
the  annual  parallax.  From  all  this  we  may  conclude,  that  as 
yet  there  are  strong  reasons  for  believing  that  the  annual  par- 
allax is  less  than  1",  at  least  with  respect  to  the  stars  hitherto 
observed. 

"  Thus  the  semi-diameter  of  the  earth's  orbit,  seen  from  the 
nearest  star,  would  not  appear  to  subtend  an  angle  of  1";  and 
to  an  observer  placed  at  this  distance,  our  sun,  with  the  whole 
planetary  system,  would  occupy  a  space  scarcely  exceeding  the 
thickness  of  a  spider's  thread. 

"  It  is  evident  that  the  stars  undergo  considerable  changes, 
since  these  changes  are  sensible  even  at  the  distance  at  which 
we  are  placed.  There  are  some  which  gradually  lose  their 
light,  as  the  star  g  of  Ursa  Major.  Others,  as  ft  of  Cetus,  be- 
come more  brilliant.  Finally,  there  are  some  which  have  been 
observed  to  assume  suddenly  a  new  splendor,  and  then  gradually 
fade  away.  Such  was  the  new  star  which  appeared  in  1572,  in 
the  constellation  Cassiopeia.  It  became  all  at  once  so  brilliant 
that  it  surpassed  the  brightest  stars,  and  even  Venus  and  Jupi- 
ter, when  nearest  the  earth.  It  could  be  seen  at  mid-day. 
Gradually  this  great  brilliancy  began  to  diminish,  and  the  star 
disappeared  in  sixteen  months  from  the  time  it  was  first  seen, 
without  having  changed  its  place  in  the  heavens.  Its  color, 
during  this  time,  suffered  great  variations.  At  first  it  was  of  a 
dazzling  white,  like  Venus ;  then  of  a  reddish  yellow,  like 
Mars  and  Aldebaran  ;  and  lastly,  of  a  leaden  white,  like  Saturn. 
Another  star  which  appeared  suddenly  in  1604,  in  the  con- 
stellation Serpentarius,  presented  similar  variations,  and  dis- 
appeared after  several  months.  These  phenomena  seem  to 
indicate  vast  flames,  which  burst  forth  suddenly  in  these  great 
bodies.  Who  knows  that  our  sun  may  not  be  subject  to  sim- 
ilar changes,  by  which  great  revolutions  have  perhaps  taken 
place  in  the  state  of  our  globe,  and  are  yet  to  take  place. 

"  Some  stars,  without  entirely  disappearing,  exhibit  varia- 

Do  the  fixed  stars  undergo  any  changes  ?    What  is  said  of  new  stars, 
and  in  what  constellations  did  they  happen  ? 


PECULIARITIES  OF    THE  FIXED   STARS.  177 

tions  not  less  remarkable.  Their  light  increases  and  decreases 
alternately,  in  regular  periods.  They  are  called,  for  this  reason, 
variable  stars.  Such  is  the  star  Algol,  in  the  head  of  Medusa, 
which  has  a  period  of  about  three  days  ;  ^  of  Cepheus,  which 
has  one  of  five  days ;  /5  of  Lyra,  six ;  v>  of  Antiuous,  seven ; 
o  of  Cetus,  334 ;  and  many  others. 

"  Several  attempts  have  been  made  to  explain  these  period- 
ical variations.  It  is  supposed  that  the  stars  which  are  subject 
to  them,  are,  like  to  all  the  other  stars,  self-luminous  bodies, 
or  true  suns,  turning  on  their  axes,  and  having  their  surfaces 
partly  covered  with  dark  spots,  which  may  be  supposed  to 
present  themselves  to  us  at  certain  times  only,  in  consequence 
of  their  rotation.  Other  astronomers  have  attempted  to  account 
for  the  facts  under  consideration  by  supposing  these  stars  to 
have  a  form  extremely  oblate,  by  which  a  great  difference  would 
take  place  in  the  light  emitted  by  them  under  different  aspects. 
Lastly,  it  has  been  supposed  that  the  effect  in  question  is  owing 
to  large  opake  bodies,  revolving  about  these  stars,  and  occa- 
sionally intercepting  a  part  of  their  light.  Time,  and  the  mul- 
tiplication of  observations,  may  perhaps  decide  which  of  these 
hypotheses  is  the  true  one. 

One  of  the  best  methods  of  observing  these  phenomena  is 
to  compare  the  stars  together,  designating  them  by  letters  or 
numbers,  and  disposing  of  them  in  the  order  of  their  brilliancy. 
If  we  find,  by  observation,  that  this  order  changes,  it  is  a 
proof  that  one  of  the  stars  thus  compared,  has  likewise  changed; 
and  a  few  trials  of  this  kind  will  enable  us  to  ascertain  which 
it  is  that  has  undergone  a  variation.  In  this  manner,  we  can 
only  compare  each  star  with  those  which  are  in  the  neighbor- 
hood, and  visible  at  the  same  time.  But  by  afterward  com- 
paring these  with  others,  we  can,  by  a  series  of  intermediate 
terms,  connect  together  the  most  distant  extremes.  This 
method,  which  is  now  practiced,  is  far  preferable  to  that  of  the 
ancient  astronomers,  who  classed  the  stars  after  a  very  vague 

What  is  understood  by  variable  stars?  How  have  astronomers  at- 
tempted to  ac««uut  for  these  appearances? 


178  ELEMENTARY   ASTRONOMY. 

comparison,  according  to  what  they  called  the  order  of  their 
magnitudes,  but  which  was,  in  reality,  nothing  but  that  of  their 
brightness,  estimated  in  a  very  imperfect  manner." 

DOUBLE     AND     MULTIPLE     STARS. 

"  There  are  stars  which,  when  viewed  by  the  naked  eye,  and 
even  by  the  help  of  a  telescope  of  moderate  power,  have  the 
appearance  of  only  a  single  star ;  but,  being  seen  through  a 
good  telescope,  they  are  found  to  be  double,  and  in  some  cases, 
a  very  marked  difference  is  perceptible,  both  as  to  their  bril- 
liancy and  the  color  of  their  light.  These  Sir  W.  Herschel 
supposed  to  be  so  near  each  other,  as  to  obey,  reciprocally,  the 
power  of  each  other's  attraction,  revolving  about  their  common 
center  of  gravity,  in  certain  determinate  periods. 


Castor.       y  Leonis.         Rigel.       Pole  Star,   n  Monoc.     $  Cancri. 

"The  two  stars,  for  example,  which  form  the  double  star 
Castor,  have  varied  in  their  angular  situation  more  than  45° 
since  they  were  observed  by  Dr.  Bradley,  in  1759,  and  appear 
to  perform  a  retrograde  revolution  in  342  years,  in  a  plane  per- 
pendicular to  the  direction  of  the  sun.  Sir  W.  Herschel  found 
them  in  intermediate  angular  positions,  at  intermediate  times, 
but  never  could  perceive  any  change  in  their  distance.  The 
retrograde  revolution  of  y  in  Leo,  another  double  star,  is  sup- 
posed to  be  in  a  plane  considerably  inclined  to  the  line  in  which 
•we  view  it,  and  to  be  completed  in  1200  years.  The  stars  5  of 
Bootes,  perform  a  direct  revolution  in  1681  years,  in  a  plane 
oblique  to  the  sun.  The  stars  f  of  Serpens,  perform  a  retro- 
grade revolution  in  about  375  years;  and  those  of  y  in  Yirgo 
in  708  years,  without  any  change  of  their  distance.  In  1802, 
the  large  star  £of  Hercules,  eclipsed  the  smaller  one,  though 

What  is  understood  by  double  stars?  Do  double  stars  revolve  about 
•ach  ether  ?  Mwtieu  the  times  of  revolution  •£  s«me  •!'  tnem. 


PECULIARITIES   OF   THE  FIXED   STARS.  179 

they  were  separate  in  1782.  Other  stars  ai;e  supposed  to  be 
united  in  triple,  quadruple,  and  still  more  complicated  systems. 
"  With  respect  to  the  determination  of  the  real  magnitude 
of  the  stars,  and  their  respective  distances,  we  have  as  yet 
made  but  little  progress.  Researches  of  this  kind  must  be 
left  to  future  astronomers.  It  appears,  however,  that  the  stars 
are  not  uniformly  distributed  over  the  heavens,  but  collected 
into  groups,  each  containing  many  millions  of  stars.  We  can 
form  some  idea  of  them,  from  those  small  whitish  spots  called 
Nebulae,  which 
appear  in  the 
heavens  as  rep- 
resented in  the 
accompanying 
illustration. 
By  means  of 
the  telescope, 
we  distinguish 
in  these  collec- 
tions an  almost 
infinite  number 
of  small  stars, 

so  near  each  other,  that  their  rays  are  ordinarily  blended  by 
irradiation,  and  thus  present  to  the  eye  only  a  faint  uniform 
sheet  of  light.  That  large,  white,  luminous  track,  which  tra- 
verses the  heavens  from  one  pole  to  the  other,  under  the  name 
of  the  Milky  Way,  is  probably  nothing  but  a  nebula  of  this 
kind,  which  appears  larger  than  the  others,  because  it  is  nearer 
to  us.  With  the  aid  of  the  telescope  we  discover  in  this  zone 
of  light  such  a  prodigious  number  of  stars  that  the  imagination 
is  bewildered  in  attempting  to  represent  them.  Yel,  from  the 
angular  distances  of  these  stars,  it  is  certain  that  the  space 
which  separates  those  which  seem  nearest  to  each  other,  is  at 
least  a  hundred  thousand  times  as  great  as  the  radius  of  the 

What  is  meant  by  Nebulae  ?     What  is  said  <pf  the  Milky  Way?     What  i» 
iU  appearance  through  a  telescope  ? 


180  ELEMENTARY  ASTRONOMY. 

earth's  orbit.  This  will  give  us  some  idea  of  the  immense 
extent  of  the  group.  To  what  distance  then  must  we  with- 
draw, in  order  that  this  whole  collection  may  appear  as  small 
as  the  other  nebulae  which  we  perceive,  some  of  which  cannot, 
by  the  assistance  of  the  best  telescopes,  be  made  to  present 
any  thing  but  a  bright  speck,  or  a  simple  mass  of  light,  of  the 
nature  of  which  we  are  able  to  form  some  idea  only  by  analogy? 
"When  we  attempt,  in  imagination,  to  fathom  this  abyss,  it  is  in 
vain  to  think  of  prescribing  any  limits  to  the  universe,  and  the 
mind  reverts  involuntarily  to  the  insignificant  portion  of  it 
which  we  are  destined  to  occupy." 

Before  we  close  this  chapter,  we  think  it  important  to  call 
the  attention  of  the  reader  to  Table  II,  in  which  will  be  seen, 
at  a  glance  (in  the  columns  marked  annual  variation),  the  gen- 
eral effect  of  the  precession  of  the  equinoxes  ;  we  here  notice 
that  all  the  stars,  from  the  6th  to  the  18th  hour  of  right  ascen- 
sion, have  a  progressive  motion  to  the  southward  ( — ),  and  all 
the  stars  from  the  18th  to  the  6th  hour  of  right  ascension,  have 
a  progressive  motion  to  the  northward  (-)-),  and  the  greatest 
variations  are  at  Oh.  and  12h.  But  these  motions  are  not,  in 
reality,  the  motions  of  the  stars  ;  they  result  from  motions  of 
the  earth.  Whenever  the  annual  motion  of  any  star  does  not 
correspond  with  this  common  displacement  of  the  equinox,  we 
say  the  star  has  a  proper  motion  ;  and  by  such  discrepancy  it 
has  been  decided,  that  those  stars  marked  with  an  asterisk,  in 
the  catalogue,  have  proper  motions;  and  the  star  61  Cygni, 
near  the  close  of  the  table,  has  the  greatest  proper  motion. 

From  this  circumstance,  and  from  the  fact  of  its  being  a 
double  star,  it  was  selected  by  Bessel  as  a  fit  subject  for  the 
investigation  of  stellar  parallax  ;  and  it  is  now  contended,  and 
in  a  measure  granted,  that  the  annual  parallax  of  this  star  is 
0".35,  which  makes  its  distance  more  than  592,000  times  the 
radius  of  the  earth's  orbit ;  a  distance  that  light  could  not 
traverse  in  less  than  nine  and  one-fourth  years. 

What  is  to  be  noticed  in  Table  II  ?  How  do  astronomers  determine  what 
starg  have  a  proper  motion  ?  What  is  said  of  the  star  61  Cygni  ? 


ABERRATION.  181 


CHAPTER   VI. 

ABERRATION,   NUTATION,  AND   PRECESSION 
OF   THE   EQUINOXES. 

ABOUT  the  year  1725,  Dr.  Bradley,  of  the  Greenwich  obser- 
vatory, commenced  a  very  rigid  course  of  observations  on  the 
fixed  stars,  with  the  hope  of  detecting  their  parallax.  These 
observations  disclosed  the  fact,  that  all  the  stars  which  come 
to  the  upper  meridian  near  midnight,  have  an  increase  of  lon- 
gitude of  about  20";  while  those  opposite,  near  the  meridian  of 
the  sun,  have  a  decrease  of  longitude  of  20";  thus  making  an 
annual  displacement  of  40".  These  observations  were  continued 
for  several  years,  and  found  to  be  the  same  at  the  same  time 
each  year  ;  and,  what  was  most  perplexing,  the  results  were 
directly  opposite  from  such  as  would  arise  from  parallax. 

These  facts  were  thrown  to  the  world  as  a  problem  demanding 
solution,  and,  for  some  time,  it  baffled  all  attempts  at  explana- 
tion ;  but  it  finally  occurred  to  the  mind  of  the  Doctor,  that  it 
might  be  an  effect  produced  by  the  progressive  motion  of  light 
combined  with  the  motion  of  the  earth  ;  and,  on  strict  exami- 
nation, this  was  found  to  be  a  satisfactory  solution. 

A  person  standing  still  in  a  shower  of  rain.  When  the  rain 
falls  perpendicularly,  the  drops  will  strike  directly  on  the  top 
of  his  head ;  but  if  he  starts  and  runs  in  any  direction,  the 
drops  will  strike  him  in  the  face  ;  and  the  effect  would  be  the 
same,  in  relation  to  the  direction  of  the  drops,  as  if  the  person 
stood  still  and  the  rain  came  inclined  from  the  direction  he  ran. 

This  is  a  full  illustration  of  the  principle  of  these  changes 
in  the  positions  of  the  stars,  which  is  called  aberration;  but  the 
following  explanation  is  more  appropriate. 

When  and  by  whom  was  Aberration,  and  Nutation  discovered?  Were 
such  results  anticipated?  Illustrate  aberration. 


182  ELEMENTARY  ASTRONOMY 

Conceive  the  rays  of  light  to  be  of  a  material  substance,  and 
its  particles  progressive,  passing  from  the  star  S  to  the  earth 

at  B  ;  passing  directly  through 
the  telescope,  while  the  telescope 
itself  moves  from  A  to  B  by  the 
motion  of  the  earth.  And  if  D 
B  is  the  motion  of  light,  and  A 
B  the  motion  of  the  earth,  then 
the  telescope  must  be  inclined  iji 
the  direction  of  AD,  to  receive 
the  light  of  the  star,  and  the 
apparent  place  of  the  star  would 
be  at  /S",  and  its  true  place  at  S, 
and  the  angle  A  DB  is  20".36,  at 
its  maximum,  called  the  angle 
of  aberration. 

By  the  known  motion  of  the 
earth  in  its  orbit,  we  have  the 
value  of  AB  corresponding  to 
one  second  of  time  :  we  have  the 
angle  ADB  by  observation  :  the 
angle  at  B  is  a  right  angle,  and 
(from  these  data),  computing 
the  side  BD,  we  have  the  velocity 
of  light,  corresponding  to  one 
second  of  time.  To  make  the 
computation,  we  have 
DB  :  BA  :  :  Rnd.  :  tan.  20".36. 

But  BA,  the  distance  which  the  earth  moves  in  its  orbit  in 
one  second  of  time,  is  within  a  very  small  fraction  of  19  miles; 
the  logarithm  of  the  distance  is  1.378802,  and,  from  this,  we 
find  that  BD  must  be  192600  miles,  the  velocity  of  light  in  a 
second ;  a  result  very  nearly  the  same  as  before  deduced  from 
observations  on  the  eclipses  of  Jupiter's  moons. 

What  is  the  greatest  auyrle  of  aberration  ?  What  truth  has  been  demon- 
strated by  ihs  aberration  «f 


ABERRATION". 


183 


The  agreement  of  these  two  methods,  so  disconnected  and 
so  widely  different,  in  disclosing  such  a  far-hidden  and  remark- 
able truth,  is  a  striking  illustration  of  the  power  of  science, 
and  the  order,  harmony,  and  sublimity  that  pervades  the  uni- 
verse. 

To  show  the  effects  of  aberration  on  the  whole  starry  heavens, 
we  give  the  figure  below.  Conceive  the  earth  to  be  moving  in 
its  orbit  from  A  to  B.  The  stars  in  the  line  AB,  whether  at 


0  or  180,  are  not  affected  by  aberration.     The  stars,  at  right 
angles  to  the  line  AB,  are  most  affected  by  aberration,  and  it 

"When,  and  in  what  position  in  respect  to  the  sun,  is  a  star  when  it  ia 
most  affected  by  aberration  ? 


184          ELEMENTARY  ASTRONOMY. 

is  obvious  that  the  general  effect  of  aberration  is  to  give  the 
stars  an  apparent  inclination  to  that  part  of  the  heavens,  to- 
ward which  the  earth  is  moving.  Thus  the  star  at  90  has  its 
longitude  increased,  and  the  star  opposite  to  it,  at  270,  has  its 
longitude  decreased,  by  the  effect  of  aberration  ;  both  being 
thrown  more  toward  180.  The  effect  on  each  star  is  20".36. 
But  when  the  earth  is  in  the  opposite  part  of  its  orbit,  and 
moving  the  other  way,  from  C  to  1),  then  the  star  at  90  is  ap- 
parently thrown  nearer  to  0  ;  so  also  is  the  star  at  270,  and  the 
whole  annual  variation  of  each  star,  in  respect  to  longitude,  is 
40".  72. 

The  supposition  of  the  earth's  annual  motion  fully  explains 
aberration ;  conversely,  then,  the  observed  variations  of  the 
stars,  called  aberration,  are  decided  proofs  of  the  earth's  annual 
motion. 

In  consequence  of  aberration,  each  star  appears  to  describe 
a  small  ellipse  in  the  heavens,  whose  semi-major  axis  is  20".36, 
and  semi-minor  axis  is  20".36  multiplied  by  the  sine  of  the 
latitude  of  the  star.  The  true  place  of  the  star  is  the  center 
of  the  ellipse.  If  the  star  is  on  the  ecliptic,  the  ellipse,  just 
mentioned,  becomes  a  straight  line  of  40". 72  in  length. 

If  the  star  is  at  either  pole  of  the  ecliptic,  the  ellipse  be- 
comes a  circle  of  40". 72  in  diameter,  in  respect  to  a  great 
circle ;  but  a  circle,  however  small,  around  the  pole,  will  in- 
clude all  degrees  of  longitude ;  hence  it  is  possible  for  stars 
very  near  either  pole  of  the  ecliptic,  to  change  longitude  very 
considerably,  each  year,  by  the  effect  of  aberration  ;  but  no 
star  is  sufficiently  near  the  pole  to  cause  an  apparent  revolution 
round  the  pole  by  aberration  ;  and  the  same  is  true  in  relation 
to  the  poles  of  the  celestial  equator. 

All  these  ellipses  have  their  longer  axis  parallel  to  the  ecliptic, 
and  for  this  reason  it  is  easy  to  compute  the  aberration  of  a 
star  in  latitude  and  longitude,  but  it  is  a  far  more  complex 

What  does  aberration  explain  ?  What  is  the  apparent  motion  of  a  star 
on  the  ecliptic  in  consequence  of  aberration?  What  is  the  apparent  motion 

•f  •ther  »tar*i? 


NUTATION.  185 

problem  to  compute  the  effects  in  respect  to  right  ascension 
and  decimation. 

The  effects  of  aberration  on  the  moon,  are  too  small  to  be 
noticed,  as  light  passes  that  distance  in  about  one  second  of 
time. 

NUTATION. 

While  Dr.  Bradley  was  continuing  his  observations  to  verify 
his  theory  of  aberration,  he  observed  other  small  variations,  in 
the  latitudes  and  declinations  of  the  stars,  that  could  not  be 
accounted  for  on  the  principle  of  aberration. 

The  period  of  these  variations  was  observed  to  be  about  the 
eame  as  the  revolution  of  the  moon's  node,  and  the  amount  of 
the  variation  corresponded  with  particular  situations  of  the 
node  ;  and,  in  short,  it  was  soon  discovered  that  the  cause  of 
these  variations  was  a  slight  vibration  in  the  earth's  axis, 
caused  by  the  action  and  reaction  of  the  sun  and  moon  on  the 
protuberant  mass  of  matter  about  the  equator,  which  gives 
the  earth  its  spheroidal  form,  and  the  effeat  itself,  is  called 
NUTATION. 

To  illustrate  this  subject,  we  give  the  following  figure  on  the 
next  page.  Let  m  represent  the  moon,  or  any  body  of  matter; 
its  attraction  on  the  ring  has  a  tendency  to  cause  the  plane  of 
the  ring  to  incline  towards  the  attracting  body,  m.  Let  the 
plane  of  the  ring\in  the  figure,  also  be  the  plane  of  the  equator, 
and  the  ring  the  protuberant  mass  of  matter  around  the  equator. 
Let  m  be  the  moon  at  its  greatest  declination,  and,  of  course, 
without  the  plane  of  the  ring. 

Let  P  be  the  polar  star.  The  attraction  of  m  on  the  ring 
inclines  it  to  the  moon,  and  causes  it  to  have  a  slight  motion 
on  its  center ;  but  the  motion  of  this  ring  is  the  motion  of  the 
whole  earth,  which  must  cause  the  earth's  axis  to  change  its 
position  in  relation  to  the  star  P,  and  in  relation  to  all  the 
stars. 

What  are  the  small  vibrations  of  the  stars,  in  latitude  and  declination, 
called  ?    What  is  the  period  of  these  vibrations  ?    What  causes  them  ? 
16 


186 


ELEMENTARY  ASTRONOMY. 


When  the  moon  is  on  the  other  side  of  the  ring,  that  is, 
opposite  in  declination,  the  effect  is  to  incline  the  equator  to 
the  opposite  direction,  which  must  be,  and  is,  indicated  by  an 
apparent  motion  of  all  the  stars. 


A  slight  alternate  motion  of  all  the  stars  in  declination,  ror- 
responding  to  the  declinations  of  the  sun  and  moon,  was  care- 
fully noted  by  Dr.  Bradley,  and  since  his  time,  has  been  fully 
verified  and  definitely  settled  :  this  vibratory  motion  is  known 
by  the  name  of  nutation,  and  it  is  fully  and  satisfactorily  ex- 
plained on  the  principles  of  universal  gravity  ;  and  conversely, 
these  minute  and  delicate  facts,  so  accurately  and  completely 
conforming  to  the  theory  of  gravity,  served  as  one  of  the  many 
strong  points  of  evidence  to  establish  the  truth  of  that  theory. 

By  inspecting  the  figure,  it  will  be  perceived  that  when  the 
sun  and  moon  have  their  greatest  northern  declinations,  all  the 
stars  north  of  the  equator  and  in  the  same  hemisphere  as  these 
bodies,  will  incline  toward  the  equator  ;  or  all  the  stars  in  that 

What  theory  is  confirmed  by  nutation  ? 


.      NUTATION.  187 

hemisphere  will  incline  southward,  and  those  in  the  opposite 
hemisphere  will  incline  northward ;  the  amount  of  vibration  of 
the  axis  of  the  earth  is  only  9". 6  (as  is  shown  by  the  motion  of 
the  stars),  and  its  period  is  18.6,  or  about  nineteen  years,  the 
time  corresponding  to  the  revolution  of  the  moon's  node.  When 
the  moon  is  in  the  plane  of  the  equator,  its  attraction  can  hjjve 
no  influence  in  changing  the  position  of  that  plane  ;  and  it  is 
evident  that  the  greatest  effect  must  be  when  the  moon's  decli- 
nation is  greatest. 

The  moon's  declination  is  greatest  when  the  longitude  of  the 
moon's  ascending  node  is  0,  or  at  the  first  point  of  Aries.  The 
greatest  declination  is  then  28°  on  each"  side  of  the  equator ; 
but  when  the  descending  node  is  in  the  same  point,  the  moon's 
greatest  declination  is  only  18°.  Hence  there  will  be  times,  a 
succession  of  years,  when  the  moon's  action  on  the  protuberant 
matter  about  the  equator  must  be  greater  than  in  an  opposite 
succession  of  years,  when  the  node  is  in  the  opposite  position. 
Hence,  the  amount  of  lunar  nutation  depends  on  the  position 
of  the  moon's  nodes. 

The  mean  course  of  the  moon  is  along  the  ecliptic :  its  varia- 
tion from  that  line  is  only  about  five  degrees  on  each  side  ; 
hence,  the  medium  effect  of  the  moon,  on  the  protuberant  mass 
of  matter  at  the  equator,  is  the  same  as  though  the  moon  were 
all  the  while  in  the  ecliptic.  But,  in  that  case,  its  effect  would 
be  the  same  at  every  revolution  of  the  moon  ;  and  the  earth's 
equator  and  axis  would  then  have  an  equilibrium  of  position, 
and  there  would  be  no  nutation,  save  a  slight  monthly  nutation, 
which  is  too  small  to  be  sensible  to  observation  ;  and  the  nuta- 
tion which  we  observe,  is  only  an  inequality  of  the  moon's 
attraction  on  the  protuberant  equatorial  ring ;  and,  however 
great  that  attraction  might  be,  it  would  cause  no  vibration  in 
the  position  of  the  earth,  if 'it  were  constantly  the  same. 

We  have,  thus  far,  made  particular  mention  of  the  moon, 
but  there  is  also  a  sofar  nutation;  its  period  is,  of  course,  a  year; 

What  must  be  the  position  of  the  moon  to  have  the  greatest  effect  ou 
nutation  ?  In  what  position  does  the  moon  have  no  effect  on  nutation? 


188          ELEMENTARY  ASTRONOMY. 

and  it  is  very  trifling  in  amount,  because  the  sun  attracts  all 
parts  of  the  earth  nearly  alike  ;  and  the  short  period  of  one 
year,  or  half  a  year  (which  is  the  time  that  the  unequal  attrac- 
tion tends  to  change  the  plane  of  the  ring  in  one  direction),  is 
too  short  a  time  to  have  any  great  effect  on  the  inertia  of  the 
earth. 

The  solar  nutation,  in  respect  to  declination,  is  only  one 
second. 

Hitherto  we  have  considered  only  one  effect  of  nutation  — 
that  which  changes  the  position  of  the  plane  of  the  equator — 
or,  what  is  the  same  thing,  that  which  changes  the  position  of 
the  earth's  axis ;  but  there  is  another  effect,  of  greater  magni- 
tude, earlier  discovered,  and  better  known,  resulting  from  the 
same  physical  cause,  — we  mean  the 

PRECESSION    OF    THE    EQUINOXES. 

We  again  return  to  first  principles,  and  consider  the  mutual 
attraction  between  a  ring  of  matter  and  a  body  situated  out  of 
the  plane -of  the  ring;  the  effect,  as  we  have  several  times 
shown,  is  to  incline  the  ring  to  the  body,  or  (which  is  the 
same  in  respect  to  relative  positions),  the  body  inclines  to  run 
to  the  plane  of  the  ring. 

The  mean  attraction  of  the  moon  is  in  the  plane  of  the  ecliptic. 
The  sun  is  all  the  while  in  the  ecliptic.  Hence,  the  mean 
attraction  of  both  sun  and  moon  is  in  one  plane,  the  ecliptic ; 
but  the  equator,  considered  as  a  ring  of  matter  surrounding 
a  sphere,  is  inclined  to  the  plane  of  the  ecliptic  by  an  angle 
of  23^  degrees,  and  hence  the  sun  and  moon  have  a  constant 
tendency  to  draw  the  equator  to  the  ecliptic,  and  actually  do 
draw  it  to  that  plane  ;  and  the  visible  effect  is,  to  make  both 
sun  and  moon,  in  revolutions,  cross  the  equator  sooner  than 
they  otherwise  w.ould,  and  thus  the  equinox  falls  back  on  tho 
ecliptic,  called  the  precession  of  the  equinoxes. 

Is  there  a  monthly  nutation?  Is  there  a  sola* nutation,  and  how  great 
is  it  ?  What  other  effect  arises  from  the  attraction  of  the  sun  and  moon,  on 
the  protuberant  mass  of  matter  about  the  equator  ? 


PRECESSION  OF  THE    EQUINOXES.  189 

The  annual  mean  precession  of  the  equinoxes  is  50".  1  of  arc, 
as  is  shown  by  the  sun  coming  into  the  equinox,  or  crossing 
the  equator  at  a  point  50".  1  before  it  makes  a  revolution  in 
respect  to  the  stars. 

If  the  moon  were  all  the  while  in  the  ecliptic,  the  precession 
of  the  equinoxes  would  then  be  a  constantly  flowing  quantity, 
equal  to  50".  1  for  each  year ;  but,  for  a  succession  of  about 
nine  years,  the  moon  runs  out  to  a  greater  declination  than  the 
ecliptic,  and,  during  that  time,  its  action  on  the  equatorial 
matter  is  greater  than  the  mean  action,  and  then  comes  a  suc- 
cession of  about  nine  years,  when  its  action  is  less  than  its 
mean;  hence,  for  nine  years,  the  precession  of  the  equinoxes 
will  be  more  than  50".  1  per  year,  and,  for  the  nine  years  follow- 
ing, the  precession  will  be  less  than  50".  1  for  each  year  ;  and 
the  whole  amount  of  variation,  for  this  inequality,  in  respect  to 
longitude,  is  17".3,  and  its  period  is  half  a  revolution  of  the 
moon's  nodes.  This  inequality  is  called  the  equation  of  the 
equinoxes,  and  varies  as  the  sine  of  the  longitude  of  the  moon's 
nodes. 

The  precession  of  the  equinoxes  causes  a  variation  of  the 
right  ascensions  and  declinations  of  all  the  fixed  stars,  as  may 
be  seen  by  inspecting  the  catalogue  of  stars  in  Table  II. 
When  any  particular  star  is  observed  to  have  a  greater  or  less 
variation  than  the  quantity  corresponding  to  the  precession, 
that  star  is  said  to  have  a  proper  motion,  as  we  have  before 
observed,  when  treating  of  the  stars. 

We  close  this  volume,  after  calling  the  attention  of  the  reader 
to  our  first  page  of  tables. 

In  common  parlance,  we  say  that  the  sun  has  no  latitude  — 
it  is  all  the  while  in  the  ecliptic  —  but  then  it  will  be  found 
that  the  sun  has  latitude,  it  deviates  north  and  south,  by  a 
quantity  too  small  even  to  be  observed;  it  is,  therefore,  a  quantity 
wholly  determined  by  theory,  and,  as  the  sun's  latitude  changes 

What  is  the  annual  mean  precession  of  the  equinoxes  ?  Has  it  an  equa 
tion?  and  if  so,  to  what  amount  ?  What  is  the  period  of  this  equation? 


190          ELEMENTARY  ASTRONOMY. 

nearly   with  the  latitude  of  the  moon,  we  must  seek  for  its 
cause  principally  in  the  lunar  motions.* 

To  understand  the  fact  of  the  sun  having  latitude,  we  must 
admit  that  it  is  the  center  of  gravity  between  the  earth  and 
moon,  that  moves  in  an  elliptical  orbit  round  the  sun  ;  and 
that  center  is  always  in  the  ecliptic  ;  and  the  sun,  viewed  from 
that  point,  would  have  no  latitude.  But  when  the  moon,  m,  is 
on  one  side  of  the  plane  of  the  ecliptic,  SO,  the  earth,  Ey 
would  be  on  the  other  side,  and  the  sun,  seen 
from  the  center  of  the  earth,  would  appear  to 
lie  on  the  same  side  of  the  ecliptic  as  the  moon. 
Hence,  the  sun  will  change  his  latitude,  when  the 
moon  changes  her  latitude. 

If  the  moon  were  all  the  while  in  the  plane 
of  the  ecliptic,  the  sun  would  have  no  latitude 
(save  some  extremely  minute  quantities,  from  the 
action  of  the  planets,  when  not  in  the  plane 
of  the  ecliptic);  but  the  moon  does  not  deviate 
more  than  5°  20'  from  the  ecliptic,  and  of 
course,  the  earth  makes  but  a  proportional  de- 
viation on  the  other  side  ;  but  in  longitude,  the 
moon  deviates  to  a  right  angle  on  both  sides, 
in  respect  to  the  sun,  and  when  the  moon  is  in 
advance  in  respect  to  longitude,  the  sun  appears  to  be  in  ad- 
vance also  ;  and  when  the  moon  is  at  her  third  quarter,  the 
longitude  of  the  sun  is  apparently  thrown  back  by  her  influence: 
the  greatest  variation  in  the  sun's  longitude,  arising  from  the 
motion  of  the  earth  and  moon  about  their  center  of  gravity,  is 
about  6"  each  side  of  the  mean. 

*  In  fact  the  sun  is  not  immovably  fixed  in  the  plane  of  the  ecliptic  :  it 
vibrates  round  the  common  center  of  gravity  of  the  solar  system. 

Jupiter  is  by  far  the  most  ponderous  planet  in  the  system,  hence  the 
center  of  gravity  between  the  sun  and  that  planet,  is  always  extremely 
near  the  plane  of  the  ecliptic,  and  the  sun's  latitude,  in  the  Nautical  Al- 
manac, is  computed  from  the  positions  of  the  moon  and  Jupiter, —  the  result 
of  each  taken  separately,  and  united. 


SEQUEL. 


A  KNOWLEDGE  of  astronomy  embraces  a  knowledge  of  the 
earth  as  a  whole,  —  and  the  external  appearance  of  the  heavens. 

The  earth  is  very  accurately  represented  by  a  globe,  and  the 
external  appearance  of  the  heavens  can  also  be  very  accurately 
represented  by  the  projection  of  each  star,  and  the  imaginary 
lines  in  the  heavens,  on  a  globe. 

Thus  we  have  a  terrestrial  and  a  celestial  globe.  Those 
whose  minds  are  at  all  cultivated,  understand  the  terrestrial 
globe,  or  the  globe  which  represents  the  earth,  at  sight,  —  but 
atlases  and  maps,  of  any  large  portions  of  the  earth,  require 
some  study,  as  the  several  parts  must  be  more  or  less  distorted, 
as  it  is  impossible  to  represent  the  surface  of  a  sphere,  accu- 
rately, on  a  plane  surface.  Hence,  no  one  can  comprehend 
maps,  unless  the  mind  refers  them  to  a  globe,  whether  the  pupil 
has  ever  actually  seen  a  globe,  or  not. 

Years  ago,  when  spherical  trigonometry  was  very  rarely 
taught,  problems  on  the  globes  were  more  attended  to,  than 
they  are  at  present.  Yet,  solutions  of  these  problems  on  the 
globes  are  very  important,  as  they  furnish  a  sure  test  of  the 
comprehension  of  the  pupil,  and  this  is  our  principal  object  in 
giving  them. 

Results  obtained  by  the  globes  are,  at  best,  but  rough  ap- 
proximations, and  no  one,  properly  disciplined,  will  claim  any 
thing  more  for  them ;  but  even  this  does  not  diminish  their 
real  importance  ;  for  this  kind  of  solution  must  go  through  the 
mind,  to  guide  us  through  the  more  exact,  scientific,  and  nu- 
merical computations. 

191 


192  SEQUEL. 


CHAPTER   I. 

PROBLEMS  TO  BE  PERFORMED   ON   THE  TERRES- 
TRIAL  GLOBE. 

PROBLEM  1.     TofinU  the  latitude  of  any  place. 

RULE. — Find  the  place  on  the  globe,  and  turn  the  globe  so  as  to  bring 
the  place  to  that  part  of  the  brass  meridian,  which  is  numbered  from  the 
equator  to  the  poles. 

The  degree  marked  on  the  meridian  above  the  place  will  be  the  latitude. 
If  the  place  be  on  the  north  side  of  the  equator,  the  latitude  will  be  north; 
if  on  the  south  side,  the  latitude  is  south. 

EXAMPLES. 

1.  What  is  the  latitude  of  the  eastern  point  of  Newfound- 
land? Ans.  46°  30'. 

2.  Required  the  latitudes  of  the  following  places : 

Florence,  Italy.  New  York,  U.  S. 

Rome,  Italy.  Boston,  U.  S. 

Bencoolon,  Sumatra.     Havana,  Cuba. 
Cadiz,  Spain.  Cape  Town,  Africa. 

Smyrna,  Turkey.          Buenos  Ayres,  S.  America. 

3.  What  places  have  no  latitude? 

4.  What  places  have  no  longitude? 

5.  What  are  the  latitudes  of  those  places  that  have  no  lon- 
gitude? 

6.  What  places  have  the  same  length  of  days  as  the  inhab- 
itants of  Edinburgh? 

Ans.  All  places  that  have  the  same  latitude  as  Edinburgh. 
A  circle  round  the  pole  in  which  Edinburgh  is  sit- 
uated, locates  the  places. 

7.  What  places  have  the  same  seasons  of  the  year  as  New 
York? 


PROBLEMS  ON  THE  GLOBES.          193 

PROBLEM  2.     To  find  the  longitude  of  any  place  on  the  globe. 

.ftuLE. — Bring  the  place  to  the  brass  meridian,  the  number  of  degrees  on 
the  equator,  reckoned  from  the  meridian  which  passes  through  Greenwich 
(England),  is  the  longitude. 

If  the  gbbe  be  placed  north  of  the  operator,  to  the  right  of  the  brass 
meridian  is  east,  to  the  left  hand  is  west. 

REMABK.  Some  American  globes  take  the  meridian  of  Washington  for 
the  first  meridian.  But  all  our  instructions  refer  to  the  meridian  of  Green- 
wich, because  both  the  English  and  American  Nautical  Almanac  refer  to 
that  meridian.  Indeed,  all  practical  men  who  use  the  English  language, 
have  adopted  that  meridian,  in  whatever  part  of  the  world  they  are,  or 
wherever  they  may  have  been  born. 

EXAMPLES. 

1.  What  is  the  longitude  of  St.  Petersburgh? 

Ans.  30°  east. 

2.  What  is  the  longitude  of  Cape  St.  Roque? 

Ans.  37°  west,  nearly. 

3.  Required  the  longitudes  of  the  following  places  : 
Aberdeen,  Scotland.         Canton,  China. 
Albany,  U.  S,  Gibralter,  Spain. 
Boston,  U.  S.  Leghorn,  Italy. 
Bombay,  E.  Indias.  Muscat,  Arabia. 

PROBLEM  3.  To  find  all  those  places  that  have  the  same  longi- 
tude as  any  given  place. 

RULE. — Bring  the  given  place  to  the  brass  meridian,  then  all  places  under 
the  edge  of  the  meridian  from  pole  to  pole,  have  the  same  longitude. 

N.  B.  Places  in  the  same  longitude  have  the  same  hour  of  the  day  at 
the  same  instant  of  absolute  time. 

EXAMPLES. 

1.  What  places  hare  the  same,  or  nearly  the  same,  longi- 
tude as  Stockholm? 

Ans.  Dantzic,  Presburg,  Toronto,  Cape  of  Good  Hope,  &c. 

2.  What  inhabitants  of  the  earth  have  midnight  when  the 
inhabitants  of  Jamaica  have  noon? 

Ans.  Pekin,  in  China,  Borneo,  the  western  part  of  Australia,  &c. 
17 


194  SEQUEL. 

3.    What  places  hare  7  o'clock  P.  M.  when  it  is  11  o'clock 
A. M.  at  London? 

Anst  All  places  having  the  longitude  of  90°  west. 

PROBLEM  4.     To  find  the  latitude  and  longitude  of  any  place. 

RULE. — Bring  the  given  place  to  that  part  of  the  brass  meridian  which  is 
numbered  from  the  equator  towards  the  poles  ;  the  degree  above  the  place 
is  the  latitude,  and  the  degree  on  the  equator,  cut  by  the  brass  meridian,  is 
the  longitude. 

N.  B.    This  problem  is  but  a  union  of  the  first  and  second. 

EXAMPLES. 

1.  What  is  the  latitude  and  longitude  of  Cape  Frio,  on  the 
eastern  coast  of  South  America? 

Ans.  Lat.  23°  S.  Lon.  42°  W. 

2.  Find  the  latitudes  and  longitudes  of  the  following  places: 
Algiers,  in  Africa.  Batavia,  in  Java. 

Aleppo,  in  Turkey.  Belfast,  in  Ireland. 

Abo,  in  Finland.  Boston,  U.  S. 

Calcutta,  India.  Cape  Desolation,  Greenland. 

PROBLEM  5.  Latitude  and  Longitude  being  given,  to  find  the 
corresponding  point  on  the  globe. 

RULE. — Find  the  longitude  of  the  given  place  on  the  equator,  and  bring 
it  to  that  part  of  the  brass  meridian  which  is  numbered  from  the  equator 
to  the  poles  ;  then  under  the  given  latitude  on  the  brass  meridian,  you  will 
find  the  place.  [Provided  the  place  is  marked  on  the  globe.] 

EXAMPLES. 

1.  What  place  has  151°  east  longitude,  and  34°  south  lati- 
tude? Ans.  Botany  Bay. 

2.  What  places  have  the  following  latitudes  and  longitudes? 
Lat.  Lon.  Lat.  Lon. 

50°    6'  1ST.         5°  54'  W.         19°  26'  N".         100°    6'  W. 
48°  12    N.       16°  16'  E.          59°  56'  N.  30°  19' E. 

55°  58'  N.         3°  12  W.  5°    9'  S.          119°  49  E. 


PROBLEMS  ON  THE  GLOBES.          195 

PROBLEM  6.  To  find  the  difference  of  latitude  between  any  two 
places. 

RULE. — If  the  two  places  are  on  the  same  meridian,  that  is,  have  the 
same  longitude,  and  are  both  north  or  boih  south  of  the  equator,  subtract 
one  from  the  other,  and  the  difference  will  be  the  difference  of  latitude. 
If  the  latitude  of  one  of  the  places  is  north  and  the  other  south,  add  the 
two  latitudes  together,  and  the  sum  will  be  their  difference  of  latitude. 

If  the  two  places  are  not  in  the  same  longitude,  find  the  latitude  of 
each  place  by  Problem  1,  and  subtract  or  add  them,  as  above  directed, 
and  you  will  have  their  difference  of  latitude. 

EXAMPLES. 

1.  What  is  the  difference  of  latitude  between  Philadelphia 
and  St.  Petersburg!!?  Ans.  20  degrees. 

2.  What   difference  of  latitude    between    Greenwich   and 
Cape  Town,  Cape  of  Good  Hope?  Ans.  85°  24'. 

3.  Required  the  difference  of  latitude  between  the  follow- 
ing places  : 

London  and  Rome.  New  York  and  New  Orleans. 

Cape  Sparteland  Cape  Verde.  Boston  and  Cape  Horn. 
Vera  Cruz  and  Cape  Horn.       Canton  and  Batavia. 

PROBLEM  7.  To  find  the  least  distance  between  any  two  places 
on  the  globe. 

RULE. — Extend  a  thread  from  one  point  to  the  other.  Apply  that  extent 
to  the  equator,  and  find  the  corresponding  number  of  degrees.  Multiply 
the  number  of  degrees  thus  found,  by  60,  for  geographical  miles,  and  by 
69.1  for  English  miles. 

EXAMPLES. 

1.  What  is  the  direct  distance  between  New  York  and 
Liverpool? 

Ans.  The  length  of  a  thread  between  the  two  places,  ap- 
plied to  a  meridian,  or  to  the  equator,  extends  over 
49  degrees,  as  near  as  we  can  determine  by  sight. 
Hence  the  distance  must  be  49  X  60=2940  geograph- 
ical miles,  or  49X69.1  =  3385.9  English  miles. 


196  SEQUEL. 

2.  What  is  the  distance  from  Cape  Cod  to  Cape  Spartel, 
the  north  west  point  of  Africa? 

Ans.  3055  geo.  miles,  or  3435  Eng.  miles. 

3.  Required  the  distances  between  the  following  places  : 
Smyrna  and  Boston.  London  and  Havana. 

Cape  Town  and  Java  Head.     Rome  and  Paris. 
From  Africa  to  South  America — nearest  points. 

REMARK.  Problems  like  the  foregoing  are  solved  by  the  rules  of  plane 
trigonometry,  in  works  of  Navigation.  Every  student  should  comprehend 
a  globe  sufficiently  well  to  form,  or  conceive,  of  the  spherical  triangle 
formed  by  the  latitudes  and  longitudes  of  the  places  :  thus,  for  example, 

The  latitude  of  New  York  is  40°  40'  N.  and  longitude  74°  W.,  and 
Liverpool  is  in  latitude  53°  25'  If.  and  3°  W. ;  what  triangle  unites  Ifcem? 

Conceive  each  locality  to  be  at  the  angular  point  of  a  spherical  triangle, 
and  the  north  pole  to  be  the  third  point. 

From  the  north  pole  to  New  York,  is  49°  20',  and  to  Liverpool  it  is  36° 
35',  and  the  angle  at  the  pole  between  these  two  meridians  is  71°.  Here, 
then,  we  have  two  sides,  and  the  included  angle  of  a  spherical  triangle, 
from  which  the  third  side  can  be  computed,  which  is  the  distance,  hi 
degrees,  between  the  two  places. 


To  solve  some  of  the  following  problems,  with  or  without  a 
globe,  the  right  ascension  and  the  declination  of  the  sun  must 
be  known.  These  elements  are  computed  and  published,  an- 
nually, in  the  American  Nautical  Almanac. 

For  those  who  have  no  access  to  an  Ephemeris,  we  subjoin 
the  following  table  of  the  sun's  declination  for  every  other  day 
of  the  year  1858,  that  being  the  second  year  after  leap  year. 
The  results  in  this  table  are  given  to  the  nearest  minute  of  arc, 
and  they  will  not  differ  many  minutes  for  the  same  day,  for  any 
other  year,  for  thirty  or  forty  years  to. come.  In  short,  results 
will  be  sufficiently  near  the  truth  to  teach  principles. 

The  table  for  the  sun's  right  ascension  is  given  on  page  6  of 
tables  in  this  volume. 


PROBLEMS  ON  THE  GLOBES. 
SUN'S    DECLINATION    FOR   1858, 


197 


But  will  serve  for  corresponding  days,  in  other  years,  for  the  purposes 
here  intended. 


D. 

January. 

February.  |    March. 

April. 

May. 

June. 

1 

23°     1'  S 

17°     6'  S 

7°  35'  S 

4°  32'  N 

15°    4'N 

22°    4'N 

3 

22°  50' 

16°  31' 

6°  49' 

5°  18' 

1  5°  40' 

22°  19' 

5 

22°  37' 

15°  55' 

6°    3' 

6°    4' 

16°  157 

22°  33' 

7 

22°  23' 

15°  18' 

5°  16' 

6°  49' 

16°  49' 

22°  46' 

9 

22°    7' 

14°  40' 

4°  30' 

7°  34' 

17°  21' 

22°  57' 

11 

21°  49' 

14°     1' 

3°  43' 

8°  19' 

17°  53' 

23°    6' 

13 

21°  29' 

13°  21' 

2°  55' 

9°    3' 

18°  23' 

23°  14' 

15 

21°    8' 

12°  40' 

2°    8' 

9°  46' 

18°  52' 

23°  20' 

17 

20°  45' 

11°  58' 

1°  21' 

10°  28' 

19°  20' 

23°  24' 

19 

20°  20' 

11°  16' 

33'  S 

11°  10' 

19°  46' 

23°  27' 

21 

19°  54' 

10°  33' 

14'  N 

11°  51' 

20°  11' 

23°  27' 

23 

19°  26' 

9°  49' 

1°    2' 

12°  32' 

20°  35' 

23°  27' 

25 

18°  58' 

9°    5' 

1°49' 

13°  11' 

20°  57' 

23°  25' 

27 

18°  27' 

8°  20'      2°  36' 

13°  50' 

21°  18' 

23°  20' 

29 

17°  56' 

I3°  23' 

14°  27' 

21°  37' 

23°  15' 

D. 

July. 

August. 

Septe'ber.    October.     November. 

December. 

1 

23°     8'  N 

18°    3'N 

8°  19'  N 

3°  11'  8.14°  27'  S 

21°  50'  S 

3 

22°  59' 

17°  32' 

7°  35' 

3°  57' 

15°     5' 

22°     7' 

5  22°  49' 

17°     1' 

6°  50' 

4°  44'     J15°42' 

22°  23' 

7;22°  37' 

16°  28' 

6°    6' 

5°  30' 

16°  18' 

22°  38' 

9  22°  9.3' 

15°  53' 

5°  20' 

6°  16' 

16°  53' 

22°  51' 

11 

22°     8' 

15°  18' 

4°  35' 

7°     1'     17°  27' 

23°     1' 

13 

21°  52' 

14°  42' 

3°  49' 

7°  46'      17°  59' 

23°  10' 

15 

21°  33' 

14°     5' 

3°    3' 

8°  31'      18°  30' 

23  J  17' 

17  21°  14' 

13°  27' 

2°  16' 

9°  15'      19°    0' 

23°  23' 

19 

20°  53' 

12°  49' 

1°  30' 

9°  59' 

19°  29' 

23°  26' 

21 

20°  30' 

12°    9' 

43'  N 

10°  42' 

19°  56' 

23°  27|' 

23 

20°    7' 

11°  29' 

4'  S 

11°  25 

20°  22' 

23°  27' 

25  19°  41' 

10°  48' 

50'     il2°    6' 

20°  46' 

23°  25' 

27  19°  15' 

10°    6' 

1°37' 

12°  48' 

21°    9' 

233  21' 

29  18°  47' 

9°  23' 

2°  24' 

13°  28' 

21°  30' 

23°  15' 

Declination  in  the  heavens  is  the  same  as  latitude  on  the 
earth.  When  the  sun  is  on  the  meridian  of  Greenwich,  in 
1858,  the  preceding  table  of  declination  shows  in  what  latitude 
the  sun  will  be  in  the  zenith  at  noon. 


198  SEQUEL. 

This  table  also  enables  us  to  solve  all  problems  like  the  fol- 
lowing, with  or  without  the  use  of  the  globes. 

1 .  On  the  3d  day  of  July,  where  on  the  earth  will  the  sun  be  verti- 
cal (or  nearly  so),  when  it  is  3  P.  M.,  apparent  time,  at  New  York? 

The  longitude  of  New  York  is  74°  west,  and  when  the  sun 
is  on  the  meridian  of  New  York,  it  is  then  apparent  noon. 
Three  hours  afterwards,  the  sun  will  be  on  the  meridian,  which 
is  45°  west  of  New  York,  or  in  the  longitude  119°  west. 

The  sun  passes  the  meridian  of  Greenwich  in  lat.  22°  59' 
north,  and  the  variation  for  one  day,  or  360°  of  longitude  is  5', 
therefore,  the  variation  for  119°  is  1'  40"  nearly. 

Whence,  when  it  is  3  P.  M.  at  New  York,  the  sun  is  vertical 
over  that  point,  on  the  earth,  whose  lat.  is  22°  57'  20"  north, 
and  Ion.  119°  west. 

2.  On  the  27/A  day  of  February,   1858,  at  9h.  12m.  P.  M.t 
apparent  time  at  Greenwich,  the  sun  and  moon  will  be  in  oppo- 
sition,* at  which  tine  there  will  be  an  eclipse  of  the  moon.     Deter- 
mine, by  the  globet  where  the  eclipse  will  be  visible. 

When  it  is  9h.  12m.  at  Greenwich,  the  sun  is  on  the  meri- 
dian 138°  west,  (computing  15°  to  each  hour,)  and  the  moon 
is  180°  from  that,  counting  either  way.  Therefore  the  moon 
must  be  on  the  meridian  in  longitude  42°  east. 

The  decimation  of  the  sun  at  that  time  will  be  8°  IT  14"  S. 

The  declination  of  the  moon,  -    9°    5'    3"  N. 

The  one  is  not  exactly  opposite  to  the  other  in  declination, 
therefore  the  moon  will  not  pass  through  the  center  of  the 
earth's  shadow,  but  53'  49"  north  of  that  center,  making  a  par- 
tial eclipse  on  the  moon's  southern  limb. 

The  moon  will  be  in  the  zenith  of  lat.  9°  7'  north,  and  Ion. 
42°  east.  Find  that  point  on  the  globe  ;  it  lies  in  upper  Egypt. 

That  point  is  the  pole  of  the  visible  eclipse,  —  that  is,  the 
visibility  will  extend  over  all  places  within  90°  of  that  point. 
Hence,  it  will  be  visible  from  all  parts  of  Africa,  Europe,  Asia 


*  This  was  written  in  1857,  therefore  in  the  future  tense. 


PROBLEMS  ON  THE  GLOBES.         199 

as  far  as  Japan,  and  the  western  part  of  New  Holland.  It  will 
be  visible  in  the  eastern  part  of  Brazil,  and  invisible  to  all 
western  America  and  the  Pacific  ocean. 

3.  July  23d,  1888,  at  6k.  A.  M.,  apparent  time  at  Greenwich, 
the  sun  and  moon  will  come  in  opposition,  and  there  will  be  an 
eclipse  of  the  moon.      Where  will  that  eclipse  be  visible,  or  where 
will  the  moon  be  nearly  vertical? 

Ans.  The  moon  will  be  nearly  vertical  in  lat.  20°  16'  south, 
and  in  longitude  90°  west. 

And  this  point  is  the  pole  of  visibility.  Hence,  the  eclipse 
will  be  visible  to  all  South  and  North  America  to  lat.  70°  north, 
and  invisible  in  the  opposite  hemisphere. 

4.  What  other  day  of  the  year  has  the  same  length  as  the  6th 
of  May?  Ans.  August  7th. 

On  the  5th  of  May,  the  sun's  declination  is  16°  15'  N.,  and 
by  inspecting  the  table,  we  find  nearly  the  same  declination  on 
•  the  7th  of  August. 

5.  What  other  day  of  tlie  year  has  the  same  length  as  the  1st 
day  of  March?  Am.  October  13th. 

PROBLEM  8.  Given  the  meridian  altitude  of  the  sun,  and  the 
sun's  declination  at  the  same  time,  to  determine  the  latitude. 

Solved  with  or  without  a  globe,  first  with  a  globe.  Suppose 
the  latitude  to  be  north. 

RULE. — Take  that  part  of  the  brass  meridian  which  is  numbered  from 
the  equator  to  the  poles ;  and  take  the  degree  on  that  meridian  corres- 
ponding to  the  sun's  declination,  north  or  south,  as  the  case  may  be.  Turn 
the  meridian,  or  so  adjust  it,  that  the  given  point  of  declination,  shall  cor- 
respond to  the  given  meridian  altitude  of  the  sun. 

Then  the  elevation  of  the  pole  above  the  horizon  will  be  the  latitude 
required. 

EXAMPLE. 

1.  Suppose  the  sun's  declination  was  20°  JV.,  and  the  sun's 
true  meridian  altitude  at  the  same  time,  was  70°  from  the  southern 
horizon.  What  was  the  latitude?  Ans.  40°  N. 


200  SEQUEL. 

I  place  the  20th  degree  of  north  declination  70  degrees  from 
the  southern  horizon.  The  equator  then  is  50°  above  the  hori- 
zon, and  consequently  the  southern  pole  must  be  40°  below 
the  southern  horizon,  and  the  northern  pole  40°  above  the 
northern  horizon,  or  the  latitude  is  40°  N. 

Without  a  globe,  the  latitude  is  computed  by  the  following 
formula : 

(90°— A)±D=Lat. 

In  this  equation,  A  represents  the  observed  meridian  altitude 
corrected  for  refraction,  semi-diameter,  and  index  error,  if  any. 
D  is  the  declination  computed  to  the  precise  time  of  observa- 
tion, (90° — A),  is  the  meridian  zenith  distance,  and  if  we 
represent  it  by  Z,  the  formula  becomes 
Z±D=Lat. 

The  plus  sign  is  used  when  the  declination  is  north,  and  the 
minus  sign  when  it  is  south.  Z  is  minus  when  the  meridian 
altitude  is  measured  from  the  northern  horizon  —  and  in  all 
cases  when  the  result  is  minus,  the  latitude  is  south. 

EXAMPLES. 

1.  The  true  meridian  altitude  of  the  sun  was  27°  32',  measured 
from  the  southern  horizon,  when  its  declination  was  6°  43'  north. 
Wliat  was  the  lalitude?  Ans.  69°  11' north. 

2.  The  true  meridian  altitude  of  the  sun  was  76°  10'  from  the 
south,  when  the  sun's  declination  was  21°  2'  north.      What  was  the 
latitude?  Ans.  34°  52'  north. 

3.  The  true  meridian  altitude  of  the  sun  was  13°  18'  from  the 
south,  when  Ihe  sun's  declination  was  19°  47'  south.    What  was  the 
latitude?  Ans.   56°  55'  north. 

4.  The  true  meridian  altitude  of  the  sun  was  76°  17'  from  the 
northern  horizon,   when  the  sun's  declination  was   23°  4'  north. 
What  ivas  the  latitude?  Ans.  9°  21'  north. 

N.  B.  In  all  the  preceding  examples  D  is  plus.  In  the 
4th  example,  Z  is  13°  43'  minus. 


PROBLEMS  ON  THE  GLOBES.          201 

5.  The  true  meridian  altitude  of  the  sun  was  53°  W  from  ike 
north,  when  the  sun's  declination  was  23°  4'  north.     What  was  the 
latitude?  Aus.   12°  48'  south. 

6.  The  true  meridian  altitude  of  the  sun  was  68°  20'  from  the 
north,  when  the  sun's  declination  was  22°  10'  south.     What  was  the 
latitude?  Ans.  30'  south. 

7.  The  true  meridian  altitude  of  the  sun  was  57°  35'  from  the 
south,  when  the  sun's  declination  was  22°  10'  south.      What  was 
the  latitude?  Ans.   10°  15' north. 

Thus  we  might  give  examples  without  end,  but  we  think 
that  we  have  sufficiently  illustrated  the  principle  of  finding 
latitude  by  meridian  altitudes. 

No  matter  what  heavenly  body  is  used,  moon,  star,  or  planet, 
provided  the  declination  of  the  object  used  is  known,  and  the 
observer  can  see  the  horizon.  Stars  are  rarely  used  for  this 
purpose,  because  the  horizon  can  rarely  be  seen  at  sea  when 
the  stars  are  visible. 

If  the  object  be  the  moon,  its  parallax  in  altitude  must  be 
taken  into  the  account ;  hence,  that  body  is  seldom  used  by  the 
common  navigator,  and  the  unscientific  observer. 

In  observatories,  zenith  distances  can  be  directly  observed. 
Observers  there,  do  not  depend  on  the  horizon. 

We  give  a  few  examples  of  finding  the  latitude  by  the  meri- 
dian zenith  distances  of  some  of  the  stars. 

8.  The  fixed  star  Spica,  was  observed  to  pass  the  meridian  of 
one  observer  2J°  3'  from  the  zenith  towards  the  south  :  to  another 
observer  it  passed  the  meridian  13°  41'  from  the  zenith  towards  the 
north .      What  was  the  latitude  of  each  observer? 

Ans.  Lat.  of  one,  10°  42'  N.;  of  the  other,  34°  2'  S. 
(N.  B.  For  the  declination  of  the  stars,  see  Table  II.) 

9.  The  fixed  star  Castor,  was  observed  to  pass  the  meridian  12° 
13'  to  the  north  of  the  zenith.      What  was  the  latitude? 

Ans.  20°  north. 


202  SEQUEL. 

10.  Suppose  the  meridian  distance  had  been  the  same  toward 
the  south,  what  would  have  been  the  latitude? 

Ans.  44°  46'  north. 

1 1 .  The  star  a,  in  Cassiopea,  whose  right  ascension  is  31  m.  49s. 
and  declination  55°  42'  north,  was  observed  to  pass  the  meridian 
(below  the  pole)  64°  20' from  the  zenith.      What  was  the  latitude? 

Ans.  59°  58'  north. 

12.  Had  the  zenith  distance  been  the  same  when  the  star  was 
above  the  pole,  measured  towards  the  north,  what  then  would  have 
been  the  latitude?  Ans.  8°  38'  south. 


PROBLEMS  ON   THE   CELESTIAL  GLOBE. 

PROBLEM  1 .  To  find  the  natural  appearance  of  the  heavens  as 
seen  from  any  given  latitude  at  any  given  hour  on  any  given  day. 

RULE. — Elevate  or  depress  the  north  pole  to  correspond  to  the  given  lat- 
itude. Find  the  sun's  place  in  the  ecliptic  for  the  given  day,  and  bring 
that  point  to  the  brass  meridian.  Set  the  index  at  12.  Then  turn  the  globe 
to  correspond  to  the  given  hour.  (Turn  westward  if  the  given  hour  is 
after  noon  —  and  eastward  if  before  noon.) 

The  position  of  the  /lobe  will  now  represent  the  true  position  of  the  heavens. 

Those  stars  that  are  near  the  brass  meridian  on  the  globe,  will  be  found 
to  be  near  the  meridian  in  the  heavens  —  and  those  stars  that  are  near  the 
eastern  horizon  on  the  globe,  will  be  found  to  be  near  the  eastern  horizon 
in  the  heavens,  <fec.  <fec. 

EXAMPLES. 

1.  At  London,  lot.  51°  30'  N.  at  2  A.  M.  on  the  20*A  day  of 
January,  what  stars  are  rising,  what  stars  are  setting,  and  what 
stars  are  on  the  meridian? 

Ans.  Lyra  and  Spica  are  rising,  Regulus  is  near  the  meri- 
dian, and  all  stars  near  the  western  horizon,  on  the 
globe,  are  setting. 

2.  Find  the  position  of  the  stars  to  an  observer  in  40°  of  north 
latitude,  on  the  1th  of  November,  at  10  o'clock  in  the  evening,  appa» 
rent  time.  Ans.  The  R.  A.  of  the  meridian  is  51m. 


PROBLEMS  ON  THE  GLOBES.          203 

That  is,  whatever  stars,  or  planets  have  the  right  ascension  of 
61  minutes,  are  near  the  meridian,  at  that  time.  As  the  right 
ascension  of  Aldebaran  is  4h.  27m.,  therefore  Aldebaran  is  3h. 
36m.  east  of  the  meridian,  or  Aldebaran  will  be  on  the  meridian 
at  1.36  A.  M.  on  the  8th  of  November. 

The  position  of  the  globe  shows  the  true  position  of  the  stars 
N.  B.  Find  the  sun's  right  ascension  for  the  given  time, 
and  ad&  the  given  hour  to  it.  Subtracting  24h.  if  the  sum  ex- 
ceeds 24.  Thus,  on  the  7th  of  November,  the  right  ascension 
of  the  sun  is  14h.  51m.,  adding  lOh.  and  rejecting  24h.,  pro- 
duces 51  minutes. 

3.      What  stars  never  set  in  latitude  40°  north? 
Ans.  All  stars,  within  40  degrees  of  the  north  pole;  and  the 
same  is  true  for  any  other  latitude. 

PROBLEM  2.  To  find  the  position  of  any  particular  star  in 
reference  to  the  meridian,  on  any  given  day,  at  any  given  hour  of 
that  day,  by  the  globe.  The  latitude  may,  or  may  not,  be  given. 

RULE. — Find  the  sun's  postion  on  the  globe  by  its  place  in  the  ecliptic 
on  the  given  day,  or  find  its  right  ascension  and  declination,  and  bring 
that  point  to  the  brass  meridian.  That  is  the  position  of  the  globe  at  noon. 
Set  the  index  at  12,  and  turn  the  globe  east  or  west,  to  correspond  to  the 
given  hour  of  the  day.  Then  look  for  the  star,  and  wherever  it  be  found 
on  the  globe,  the  corresponding  point  in  the  heavens  will  be  its  place.  And 
if  the  globe  be  placed  where  a  fair  view  of  the  heavens  can  be  had,  and 
the  brass  meridian  placed  north  and  south,  and  the  pole  elevated  to  cor- 
respond with  the  latitude  of  the  place,  then  a  line  from  the  center  of  the 
globe  through  the  star,  on  the  globe,  continued  to  the  heavens,  will  point 
out  the  star,  or  pass  very  near  it. 

WITHOUT    THE    GLOBE. 

RULE. — Subtract  the  right  ascension  of  the  sun  from  the  right  ascension 
of  the  star,  and  the  remainder  is  the  apparent  time  when  the  star  comes  to 
the  meridian.  This  time,  compared  with  the  given  time,  will  determine 
whether  the  star  is  east  or  west  of  the  meridian,  and  how  far. 

EXAM  PLES. 

1.  On  the  \Qth  of  January,  what  is  the  position  of  the  dog  star 
Sirius,  at  9  P.  M.,  apparent  time? 

Ans.  2h.  14m.  east  of  the  meridian. 


24  SEQUEL. 

N.  B.  On  the  11'h  of  January,  at  9  P  M.,  the  right  ascension  of  the  sun 
is  never  far  from  19h.  25m.,  and  the  right  ascension  of  Sirius  is  6h.  39m. 
Whence  24+(G+39),  or  30h.  39ra.— 19h.  25m.  -Ilk.  14m.  That  is,  on 
that  day  of  the  year,  Sirius  comes  to  the  meridian  not  far  from  14m.  past 
eleven,  apparent  time  ;  therefore,  at  9  P.  M.  it  must  be2h.  and  14m.  east  of 
the  meridian  —  whatever  be  the  latitude  of  the  observer. 

2.  What  is  the  position  of  Antares  at  1 0  P.  M.  on  the  4th  of 
July?  Ans.  It  is  35m.  west  of  the  meridian. 

REMARK. — "We  find  the  time  when  the  moon  or  a  planet  will  pass  the 
meridian,  on  the  same  principle  as  we  find  the  time  for  a  star,  except  that 
we  must  be  more  particular  —  as  the  right  ascensions  of  the  moon  and 
planets  change,  and  the  stars  are  supposed  to  be  fixed. 

We  must  have  the  right  ascension  of  sun  and  planet  at  the  exact  time 
when  the  planet  passes  the  meridian. 

But  we  can  illustrate  more  clearly  by  the  following  example  : 

On  the  5th  of  August,  at  noon,  Greenwich  time,  the  right  ascen- 
sion of  the  sun  was,  by  the  Nautical  Almanac,  9h.  %m.  355.36, 
and  the  hourly  variation  was  9s. 59. 

The  right  ascension  of  the  moon,  at  the  same  time,  was  1 2/i.  1 9m. 
38s.2,  and  the  hourly  increase  was  \m.  445.4.  At  what  lime  did 
the  moon  pass  the  meridian  of  75°  west  longitude,  on  that  day? 

h.    m.      s. 
From  Q)  right  ascension,       -         -         -     12  19  38.20 

Subt.  @  right  ascension,  9     2  35.36 

ApproA.  time  Q)  passes  Gr.       -         -  -       3  17     2.84 

Add  for  Lon.  75°  W.  _6 

Correction  to  be  made  for        -         -  -     8  17     2 
Q)  R.  A.  increases,  per  hour,  1m.  44s. 4 
Q  R.  A.  increases,  per  hour,           9s. 59 

Variation  per  hour,  1m.  34s. 81    and  this  for  8|£h. 

gives  a  variation  of  13m.  5s.  28. 

h.    m.    s. 
Whence,  to  the  approx.  time  at  Gr.     3   17  2.84 

Add  13  5.28 

Q)  passes  merid.  in  Lon.  75°  W.  at  3  30  8.12  app.  time.* 

Equation  of  time,  add  5  40 

Q)  passes  merid.  of  Lon.  75°  W.  at  3  35  48     mean  time. 

*  To  be  perfectly  accurate,  we  should  correct  for  8k.  30m.  8s.,  or  correct 
twice. 


PROBLEMS  ON  THE  GLOBES. 


205 


PROBLEM  3.  To  find  the  time,  on  any  particular  day,  when 
any  heavenly  body,  whose  declination  is  given,  will  rise  and  set. 

We  must  first  find  the  time  that  the  given  body  passes  the  meridian,  as 
taught  in  the  foregoing  examples.  Then  we  must  obtain  the  semi-diurnal 
arc,  which  is  the  time  required  for  a  body  to  pass  from  the  horizon  to  the 
meridian,  or  from  the  meridian  to  the  horizon,  and  this  interval  depends  on 
the  declination  of  the  body,  and  the  latitude  of  the  place  from  which  it  is 
observed. 

When  the  declination  of  a  body  is  zero,  that  is,  on  the  celestial  equator, 
the  semi-diurnal  arc  is  six  hours,  observed  from  all  localities. 

When  the  latitude  and  declination  are  both  north,  or  both  south,  that 
interval  is  greater  than  six  hours. 

When  the  latitude  and  declination  are  on  opposite  sides  of  the  equator, 
the  semi-diurnal  arc  is  always  less  than  six  hours. 

The  difference  between  six  hours  and  the  semi-diurnal  arc  is 
called  Ascensional  Difference,  and  its  values  will  be  found  in 
the  following  table,  corresponding  to  various  declinations,  from 
1°  to  27°.  Under  the  declination,  and  opposite  the  latitude, 
will  be  found  the  corresponding  ascensional  difference. 

For  a  practical  work,  a  more  complete  table  would  be  given. 
DELINATION  OF  @,  Q),  ~fc,  OR  PLANET. 


Lat. 

l  3°  6° 

9u<10°j  12° 

14- 

16W 

18^ 

20  J  i  22° 

23y  :  24^ 

25°    26°(27P 

m 

m 

m 

m!  nil  to 

m 

m 

m 

m     m 

m 

m 

m 

m 

m 

18 

4   8 

12!  13!     16 

19 

21 

29 

27      40 

32 

33 

35 

36 

38 

21 

2 

5 

914'  16'     19 

22 

25 

33 

32     96 

38 

39 

41 

43 

45 

24 

o 

5 

11  16    18 

21 

26 

29 

39 

37 

41 

44 

46 

68 

50 

52 

27 

2 

61219    21 

25 

29 

34 

43 

43 

43 

50 

52 

53 

58 

50 

h 

h 

h 

h 

30 

2 

7 

1421 

23 

28 

33 

38 

49 

49 

54 

57 

1     01    2 

1     51     8 

h 

h 

33 

3 

81624 

26 

32 

37 

43 

55 

55 

1     1 

1     4 

1     71  11 

1  14 

1  17 

|     i 

h 

36 

3 

94826 

29 

36 

42 

48 

1     1 

1     81  12 

1  161  191  23 

1  27 

I 

h 

\ 

39 

3 

102029 

33 

40 

47 

54 

1     1 

1     9 

1  16  1  20 

1  25 

1  291  33 

1  37 

42 

4 

1  1  !22  33 

37 

44 

h 
521     0 

1     P 

1  17 

1  251  30 

1  35 

1  391  44 

1  48 

4."> 

412 

2439    41 

49 

581     7 

1  16 

1  25 

1  35  1  40  1  46  1  51  1  57  2    3 

A 

48 

413 

2844 

45 

55 

1     4.1  14 

1  25 

1  35 

1  471  531  592    52  112  28 

h 

51 

514 

3045 

501     1 

7  121  23 

1  35 

1  47 

2     02     62  132  212  24'2  36 

52 

SM15 

3.1  47 

521     31   14 

1  26 

1  38 

1  51 

•2     52  122  192  272  35,2  43 

53 

5:16 

32  49 

541     6 

1   17 

1  29 

1  42 

1  56 

2   102  172  25 

2  33  2  49i2  58 

54 

617 

33  50    56  1     8 

1  20 

1  331   462     02  152  232  31 

2  402  571  3     7 

206  SEQUEL. 

EXAM  PLES. 

1.  On  the  10th  day  of  January,  1858,  the  right  ascensisn  of 
the  planet  Jupiter  will  be  2/i.  16m.  525.,  and  declination  12°  32' 
north.  The  right  ascension  of  the  sun,  at  the  same  time,  will  bo 
\Qh.  28m.  nearly.  What  time  will  the  planet  pass  the  meridian, 
and  what  lime  will  it  rise  and  set,  observed  from  latitude  42°  north? 

h.    m.    s. 

From  the  R.  A.  of  Jupiter,  +24h.          26  16  52 
Subt.  the  R.  A.  of  sun,         -         -          19  28 


Apparent  time  that  Jupiter  passes  mer.        6  48  52   P.  M. 
To  6h.  add  Ascensional  diff.  45m.         -       6  45 


Jupiter  rises,  (apparent  time, )  -  3  52  P.  M. 

Jupiter  sets,  (next  morning,)  at  1   33  52  A.  M. 

2.  What  time  (approximately)  will  Sirius  rise,  pass  the  mer* 
dian,  and  set,  on  4th  of  March,  observed  from  New  York? 

h.    m. 

FromR.  A.  Sirius  +24h.  (see  Tab.  II,)      30  39  nearly. 
Subt.  R.  A.  of  sun,  (see  p.  6,  of  Tables)      23     1  nearly. 

Sirius  passes  meridian,  apparent  time,          7  38  P.  M. 
From  6h.  take  Ih.  nearly,  (semi-diur.  arc,)     5 

Sirius  rises  at  2  38  P.  M. 

Sirius  sets  next  morning  at  0  38  A.  M. 

Thus  we  might  operate  with  any  planet,  or  star. 

The  moon  requires  more  care  ;  we  must  have  its  right  as- 
cension and  declination,  at  times,  as  near  that  of  rising  and 
setting,  as  we  can  procure,  and  also,  take  parallax  into  account. 


TABLES.  l 

EXTRACTS    FROM   THE   NAUTICAL   ALMANAC   POR    JANUARY,    1846. 


. 

THE  SUN'S 

_£  *Urt 

0 

Apparent 

oi  tne 
Radius 

THE  MOON'S 

• 

Vector 

9 

"5 

Longitude. 

Latitude. 

of  the 
Earth. 

Longitude. 

Latitude. 

Semi- 
diam. 

Hor. 
Paral. 

Q 

Noon. 

Noon. 

Noon. 

Noon. 

Noon. 

Noon. 

Noon. 

1 

O       1        II 

280  46  15.3 

n 

N.0.49 

9.99266 

o            // 

330  42  13.9 

o      /       // 

N.4  54    8.5 

16  21.6 

/      n 

60    2.3 

2 

281  47  26.1 

0.45 

9.99266 

445    7  12.0 

4  24    8.7 

16    8.3 

59  13.5 

282  48  36.5 

0.37 

9,99267 

359    4  55.4 

3  39    5.9 

15  53.9 

58  20.5 

4 

283  49  46.5 

0.27 

9.99267 

12  35  34.7 

2  43     1.9 

15  39.8 

57  28.7 

O 

284  50  56.1 

0.1G 

J.!)9268 

25  41  31.5 

1  39  55.7 

15  26.7 

56  40.8 

6 

285  52    5.3 

N.0.03 

9.99268 

38  26  25.0 

N.O  33  28.3 

15  15.2 

55  58.7 

m 

286  53  13.9 

S.  0.11 

9.99270 

50  54  23.2 

S.O  33    36 

15    5.6 

55  23.3 

8 

287  54  22.0 

0.25 

9.99271 

63    9  30.1 

1  36  46.8 

14  57.6 

54  54.1 

y 

288  55  29.7 

0.38 

9.99272 

75  15  21.8 

2  35    8.6 

14  51.5 

54  31.6 

10 

289  56  36.8 

0.49 

9.99274 

87  14  56.3 

3  25  55.4 

14  46.9 

54  14.6 

11 

290  5V  43.4 

0.58 

9.99277 

99  10  31.3 

4    7  13.7 

14  43.8 

54    3.3 

12 

291  58  49-5 

0.65 

9.99279 

111     3  50.8 

4  37  30.7 

14  42.1 

53  57.0 

13 

292  59  55.3 

0.70 

9.99282 

122  56  17.6 

4  55  38.9 

14  41.7 

53  55.7 

14 

294    1     0.5 

0.71 

9.99285 

134  49     7.9 

5     0  564 

14  42.8 

53  59.8 

i: 

295    2    5.4 

0.69 

9.9928t 

146  43  48.4 

4  53    7.6 

14  45.5 

54    9.7 

16 

296    3    9.9 

0.64 

9.99292 

158  42  11.3 

4  32  23.1 

14  50.0 

54  26.0 

17 

297    4  14.0 

0.57 

9.99295 

170  46  44.8 

3  59  17.1 

14  56.3154  49.0 

18 

298    5  17.8 

0.47 

9.99299 

183    0  38.7 

3  14  47.1)15    4.6 

55  19.7 

19 

299     6  21.21       0.35 

9.99304 

195  27  41.8 

2  20  14.215  15.2 

55  58.4 

2( 

300     7  24.21       0.23 

9.99308 

208  12  10.4 

1  17  27.8 

15  27.756  44.4 

21 

301     8  26.7J  S.0.09 

9.99313 

221  18  27  5 

S.O    8  53.1 

15  42.0 

57  37.0 

j 

I 

22 

302    9  28.9 

N.0.04 

9.99318 

234  50  26.7 

N.I     2  20.515  57.3 

58  32.9 

2: 

303  10  30.4 

0.15 

9.99323 

248  50  42.5 

2  12  11.716  12.5 

59  28.8 

2- 

304  11  31.31       0.25 

'1.99328 

263  19  30.4 

3  15  50.9  16  26.2 

60  iy.o 

i 

25 

305  12  31.5 

0.33 

9.99334 

278  13  48.8 

4    8    2.8 

16  36.8 

60  57.9 

26 

306  13  30.9 

0.38 

9.9:)339 

293  26  49.2 

4  43  49.4 

16  42.9 

61  20.2 

27 

307  14  29.3 

0.40 

9.99345 

308  48  22.8 

4  59  32.416  43.5 

61  22.6 

98 

308  15  26.8 

0.40 

9.99351 

:;24    6  34.0 

4  53  45.4 

16  38.7 

61     4.9 

29 

309  16  23.3 

0.37 

9.99357 

339     9  55.3 

4  27  32.S 

16  28.960  29.1 

30 

310  17  18.5 

0.30 

•1.9936: 

353  49  32.0 

3  44    %.<< 

16  15.6 

59  40.2 

31 

311  18  12.6 

0.21 

9.99369 

8    0  13.1 

2  47  5e.l 

16    0.2 

58  487 

32 

312  19    5.3J  N.0.10 

9.99.7J  5 

21  40  34.3 

N.I  43  50.( 

515  44.2 

57  45.1 

TABLES. 


TABLE   I. 

MEAN   ASTRONOMICAL   REFRACTIONS. 
Barometer  30  in.     Thermomefer,  Fah.  50°. 


Ap.  Alt. 

Rcfr. 

Ap.  Alt. 

Refr. 

Ap.  Alt. 

Reft. 

Alt. 

Refr. 

0°  0' 

33'  51" 

4-'  0' 

11'  52" 

12*  0' 

4'  2>U" 

42W 

1  4.6' 

5 

32  53 

10 

11  30 

10 

4  24.4 

43 

1  2.4 

V 

31  58 

20 

11  10 

20 

4  20.8 

44 

1  0.3 

Jl5 

31  5 

30 

10  50 

30 

4  17.3 

45 

0  58.1 

fji) 

30  13 

40 

10  32 

40 

4  13.9 

46 

56.1 

25 

29  24 

50 

10  15 

50 

4  10.7 

47 

54.2 

30 

28  37 

5  0 

9  58 

13  0 

4  7.5 

43 

52.3 

35 

27  51 

10 

9  42 

10 

4  4.4 

49 

50.5 

40 

27  6 

20 

Q  27 

20 

4  14 

50 

48.8 

45 

26  24 

30 

9  11 

80 

3  5K4 

51 

47.1 

50 

25  43 

40 

8  58 

40 

3  55.5 

52 

45.4 

55 

25  3 

50 

8  45 

50 

3  52.6 

53 

43.8 

1  0 

24  25 

6  0 

8  32 

14  0 

3  49.9 

54 

42.2 

5 

23  48 

10 

8  20 

10 

3  47.1 

55 

40.8 

10 

23  13 

20 

8  9 

20 

3  44.4 

56 

39.3 

15 

22  40 

30 

7  58 

30 

3  41.8 

57 

37.8 

20 

22  8 

40 

7  47 

40 

3  39.2 

i)8 

36.4 

25 

21  '37 

50 

7  37 

50 

3  36.7 

59 

35.0 

30 

21  7 

7  0 

7  27 

15  0 

3  34.3 

60 

33.6 

35 

20  28 

10 

7  17 

15  30 

3  27.3 

B] 

32.3 

40 

20  10 

2!) 

7  8 

16  0 

3  20.6 

62 

31.0 

45 

19  43 

30 

6  59 

16  30 

3  14.4 

63 

29.7 

50 

19  17 

40 

6  51 

17  0 

3  8.5 

64 

28.4 

55 

18  52 

50 

6  43 

17  30 

3  2.9 

65 

27.2 

2  0 

18  29 

8  0 

6  35 

18  0 

2  57.6 

66 

25.9 

5 

18  5 

10 

6  28 

19 

2  47.7 

67 

24.7 

10 

17  43 

20 

6  21 

20 

2  38.7 

68 

23.5 

15 

17  21 

30 

6  14 

21 

2  30.5 

69 

22.4 

20 

17  0 

40 

6  7 

22 

2  23.2 

70 

21.2 

25 

16  40 

50 

6  0 

23 

2  16.5 

71 

19.9 

30 

16  21 

9  0 

5  54 

24 

2  10.1 

72 

18.8 

35 

16  2 

10 

5  47 

25 

2  4.2 

73 

17.7 

40 

15  43 

20 

5  41 

26 

58.8 

74 

16.6 

45 

15  25 

30 

5  36 

27 

53.8 

75 

15.5 

50 

15  8 

40 

5  HO 

28 

49.1 

76 

14.4 

55 

14  51 

50 

5  25 

29 

44.7 

77 

13.4 

3  0 

14  35 

10  0 

5  2U 

30 

40.5 

78 

12.3 

5 

14  19 

10 

5  15 

31 

36.6 

79 

11.2 

10 

14  4 

20 

5  10 

32 

33J) 

80 

10.2 

15 

13  50 

30 

5  5 

33 

29.5 

PI 

9.2 

20 

13  35 

40 

5  0 

34 

26.1 

F2 

8.2 

25 

13  21 

50 

4  56 

35 

23.0 

b3 

71 

30 

13  7 

11  0 

4  51 

36 

20.0 

t-4 

6.1 

35 

12  53 

10 

4  47 

37 

13.1 

F5 

,r;.l 

40 

19  41 

20 

4  43 

38 

14.4 

b6 

4.1 

45 

12  28 

30 

4  39 

39 

1  11.8 

87 

3.1 

50 

12  16 

40 

4  35 

40 

1  9.3 

88 

2.0 

55 

12  3 

50 

4  31 

41 

1  6.9 

89 

1-0 

TABLE   C. 

CORRECTION  OF  MEAN  REFRACTION. 
Hight  of  the  Thermometer. 


—  - 

24° 

28o 

320 

360 

40° 

44° 

52" 

56° 

60^ 

640 

68° 

72° 

Jt>o 

800 

Lit.' 

H 

/  a 

,  „ 

„ 

„ 

„ 

„ 

„ 

0  '  ' 

0.10: 
u.Oi) 
0.2:) 
0.30 
0.40 
0.50 
i.OO 
1.10 
1.20 
1.30 
1.40 
1.50 
2.00 
2.20 
2.40 
3.00 
3.20 
3.40 
4.00 
430 
5.00 
5.30 
6.00 
6.30 
7.00 

Q 

i.  12 
.05 
.59 
.53 
.48 
.43 
.38 
.33 
.29 
.25 
.21 
.18 
.11 
.06 
.01 
57 
53 
49 
45 
41 
38 
35 
33 
31 
27 

1.55 
1.49 
1.44 
1.39 
1.34 
1.29 
1.25 
1.21 
1.17 
1.14 
1.11 
1.08 
1.05 
1.00 
55 
51 
47 
44 
41 
38 
35 
32 
30 
28 
26 
23 

^28 
.24 
.20 
.16 
.12 
.09 
1.06 
1.03 
l.OC 
57 
55 
53 
48 
44 
41 
38 
36 
33 
31 
28 
26 
24 
22 
21 
19 

1.11 
1.08 
1.04 
1.01 
58 
55 
53 
50 
48 
46 
44 
42 
39 
37 
34 
32 
29 
28 
26 
24 
22 
20 
19 
17 
16 
15 

51 
48 
46 
44 
42 
40 
38 
36 
34 
32 
31 
30 
29 
26 
24 
22 
21 
20 
18 
17 
16 
14 
13 
12 
12 
10 

31 
29 
28 
26 
25 
24 
23 
22 
21 
20 
18 
17 
17 
16 
14 
13 
13 
12 
11 
10 
9 
9 
8 
7 
7 
6 

10 
9 
9 
8 
8 
8 
7 
7 
6 
6 
6 
6 
5 
5 
5 
4 
4 
4 
4 
3 
3 
3 
2 
2 
2 
2 

29 
27 
26 
25 
24 
23 
21 
20 
19 
18 
18 
17 
16 
15 
14 
13 
12 
11 
10 
9 
9. 
8 
7 
7 
6 
5 

48 
45 
44 
41 
39 
37 
36 
34 
32 
31 
30 
28 
27 
25 
23 
21 
20 
18 
17 
16 
14 
13 
12 
11 
10 
9 

1.07 
1.04 
1.01 
58 
55 
52 
50 
48 
45 
43 
41 
39 
37 
35 
32 
30 
28 
26 
24 
22 
20 
19 
17 
15 
14 
13 

1.25 
1.21 
1.17 
1.13 
1.10 
1.06 
1.03 
1.00 
57 
54 
52 
50 
48 
44 
41 
38 
35 
33 
31 
28 
26 
24 
22 
20 
19 
16 

.43 
.38 
.33 
.28 
.24 
.20 
.17 
.13 
.09 
.06 
.04 
.01 
58 
54 
50 
46 
43 
40 
37 
34 
31 
29 
26 
24 
23 
20 

2.01 
.54 
.49 
.43 
1.38 
.34 
1.30 
1.26 
1.21 
1.18 
1.15 
1.11 
1.08 
1.03 
58 
54 
50 
47 
44 
40 
36 
34 
31 
29 
27 
24 

2.19 
2.12 
2.05 
1.59 
1.53 
1.48 
1.43 
1.38 
1.33 
1.29 
1.25 
1.21 
1.18 
1.11 
1.06 
1.01 
57 
53 
50 
45 
40 
38 
35 
33 
31 
27 

9 

24 

20 

16 

13 

9 

5 

2 

5 

8 

11 

14 

18 

21 

24 

10 

22 

20 

18 
17 

15 
14 

12 
11 

8 
8 

5 
5 

1 

1 

4 

4 

7 

7 

10 
9 

13 
12 

16 
15 

19 

18 

22 
20 

12 

18 

15 

13 

10 

7 

4 

1 

4 

6 

9 

11 

13 

16 

18 

13 

17 

14 

12 

i 

7 

4 

1 

3 

6 

8 

10 

12 

15 

17 

14 

16 

13 

11 

8 

6 

4 

1 

3 

5 

7 

c 

11 

14 

16 

15 

15 

12 

10 

8 

6 

3 

1 

3 

5 

1 

£ 

11 

13 

15 

16 

14 

12 

c 

• 

5 

3 

1 

3 

5 

6 

8 

10 

12 

14 

17 

IS 

1 

( 

' 

5 

3 

1 

3 

4 

6 

8 

j 

11 

13 

1  4 

18 

12 

11 

8 

1 

5 

3 

1 

2 

4 

6 

j 

( 

10 

12 

19 

11 

8 

1 

4 

3 

1 

2 

4 

5 

' 

8 

10 

11 

20 

11 

i 

6 

4 

2 

1 

2 

4 

t 

6 

8 

9 

11 

21 

10 

i 

• 

5 

4 

2 

1 

2 

3 

i 

6 

' 

9 

10 

j*A 

22 

1C 

• 

5 

4 

2 

1 

2 

3 

r 

6 

' 

8 

10 

*** 
23 

c 

i 

5 

4 

2 

1 

2 

3 

i 

6 

' 

8 

9 

24 

( 

5 

3 

2 

1 

2 

3 

t 

t 

1 

8 

9 

25 

i 

5 

3 

2 

1 

2 

3 

i 

» 

1 

7 

8 

s 

4 

3 

2 

1 

2 

3 

i 

i 

1 

7 

t 

27 

5 

4 

3 

2 

1 

2 

3 

i 

r 

( 

7 

: 

28 

•J 

4 

3 

2 

0 

1 

2 

'i 

c 

t 

6 

1 

30 

- 

4 

3 

2 

0 

I 

2 

3 

1 

5 

6 

7 

28.2 

28.5C 

>  28.8o 

291 

29.75 

30.  Oa 

30.35 

30.64 

30.93 

Higlit  of  the  Barometer. 

18 


TABLES. 
TABLE    II. 

MEAN  PLACES  FOR  100  PRINCIPAL  FIXED  STARS,  FOR  JAN.  1,  1846. 


Star's  Name. 

u 

CO 
% 

Right  Ascen, 

Annual  Yar 

Declination. 

Ann.  Van 

«t  ANDROMED^E 

1 

2.3 
3 
3 

2.3 
2.3 
3 
1 

3 
3 
o  s 

0  0  26.257 
0  5  18.691 
0  17  34.168 
0  31  48.294 

0  35  51.339 
1  3  52.226 
1  16  19.692 
1  31  58.291 

1  58  30.193 
2  35  19.633 
2  54  14.072 
3  13  21.403 

3  38  20.382 
3  50  50.760 
4  27  5.404 
5  5  19.317 

5  7  8.383 
5  16  33.662 
5  24  8.428 
5  25  56.406 

5  28  24.062 
5  34  4  531 
5  46  50.189 
6  13  38.621 

6  20  32.145 
6  26  30.287 
6  38  21.883 
6  52  34.440 

7  10  55.298 
7  24  46.065 
7  31  14.2.37 
7  35  53.153 

8  0  59.232 
8  38  37  154 
8  48  38.088 
9  12  58.192 

9  20  1.170 
9  22  31.453 
9  37  6.098 
0  0  10.062 

+  3.0720 
3.0784 
3.3054* 
3.3418 

+  2.9995 
17.1346* 
3.0015 
2.2339 

+  3.3475 

3.1085 
3.1266 
4.2324 

+  3.5473 

2.7898 
3.4274 
4.4082 

+  2.8787 
3.7827 
3.0609 
2.6425 

+  3  0404 
2.1691 
3.2433 
3.6257 

+  1.3279 
30.7946 
2.6459* 
2.3558 

+  3.5918 
3.8561 
3.1445* 
3.6829* 

+  2.5596 
3.1966 
4.1261* 
1.6100 

+  2.9499 
4.0504* 
3.4258 
+  3.2211 

(leg.     niin.     sec. 

N.28  14  25.40 
N.14  19  37.80 
S.78    7  24.40 
N.55  41  31.08 

S.18  49  59.01 

+280.'055 
20.050 
19.997 
19.862 

4-19.810 
19.279 
18.952 
18.461 

+17.432 
15.621 
14.532 
13.329 

+11.620 
10.711 
7.097 
4.737 

+  4.583 
3.776 
3.123 
2.968 

+  2.754 
2.262 
+  1.149 
—  1.196 

—  1.796 
2.337 

4.484* 
4.562 

—  6.110 
7.253 

8.758* 
8.152 

—10.10-1 
12.800 
13.464 
14961 

—15.366 
1  6.108* 
16.283 
-17.377 

y  PEGASI  (Algenib),..  .  . 
&  Hydri,  

$  Ceti,  

a  URS.  MiN.  (Polaris),. 
61  Ceti 

N.88  29  17.88 
S.   8  58  45  93 
S.58     1  14.34 

N.22  43  53.86 
N.  2  35     1.17 
N.  3  28  55.70 
N.49  18  28.20 

N.23  37  27.73 
S.  1357     1.50 
N.16  11  41.39 
N.45  50    6.56 

S.    8  23    3.33 
N.28  28  17.49 
S.   0  25    4.86 
S.  17  56  12.77 

S.   1  18  17.53 
S.34    9  36.95 
N.  7  22  22.32 
N.22  35  13.16 

S.52  36  49.17 
N.87  15  31.20 
S.  16  30  32.83 
S.  28  45  59.38 

N.22  15  37.47 
N.32  13  12.93 
N.  5  36  54  95 
N.28  23  34.06 

S.23  51  50.94 
N.  6  58  48.51 
N.48  38  32.35 
S.58  37  49.78 

S.    7  59  39.05 
N.52  22  31.09 
N.24  28  49.46 
N.12  43    2.96 

«t  Eridani  (Achernar),. 
a.  ARIETIS    •  •  •  

y  Ceti,  

o  3 

»  Tauri,  

3 

2.3 
1 
1 

1 
2 
2 
3.4 

2.3 
2 

1 
3 

1 
6 

1 
2.3 

3.4 
3 

1  .2 
2 

3.4 
4 
3.4 
2 

2 
3 
3 
1 

«  J  Eridani,  

ee  TAURI,  (Aldebarari)  ,.  . 
a.  AuRlUJE,  (Capella),..  . 

0  ORIONIS,  (Rigel),  
10  TAURI,  

fj.  Gcminorum,  

«  Argus,  (Canopus),.  .  . 
51  (Hev.)  Cephei 

a  CAMS  MAJ.,  (Sirius), 
i  Canis  Majoris  

J  Gerntnoruni  

a2  GEMINOR.  (Castor),... 
a  CAN.  MIN.,  (Procyon), 
$  GEMINOR,  (Pollux),.. 

t  Hydrae,  

/  Urs»  Majoris,  

v.  HYDROS  

«  LEONIS,  (Regulus),.  .  . 

TABLE   II. 


Star's  Name. 

g 

£ 

Right  Ascen, 

Annual  Var. 

Declination. 

Ann.  Var. 

2 

t) 

3 
3.4 

2 
5 
1 

2  £ 

2^3 
1 
2  [ 

3 

1 
1 

1 

3 
3 
3 

2  .3 

2 

2  .3 
4 
2 

3 
1 

3 
2 

4 
3.4 
6 
2 

2 
2 
3. 
3 

1 
3 
3 
3. 

3 

3'. 
3 

0  39     6.223 
0  54  10.737 
1     5  54.583 
1  11  38.718 

1  41  12.066 
1  45  42.219 
2    9  26.893 
12  18    4.916 

12  26  18.465 
12  48  49  007 
13  17    5.233 
13  41  27.894 

13  47  21.140 
13  53    0.800 
14    8  38.366 
14  29  11.925 

14  38  15.706 
14  42  22.132 
14  51  13.199 
15    8  43.595 

15  28  10.083 
15  36  41  077 

4-  2.3051 
3.8001 
3.1928 
3.0010 

+  3.0654* 
3.1874 
3.3409 
3.2710 

+  3.1342 
2.8403 
3.1512 
2.3525* 

+  2.8606 
4.1508 
2.7336* 
4.0165* 

+  2.6229 
-+-  3.3102 
—  0.2692 
+  3.2226 

+  2.5279 
+  2.9391 
—  2.3520 
+  3.4742 

+  3.1382 
3.6638 
0.7960 
+  6.2587 

—  6.5328* 
+  2.7320 
106.8627 
1.3513 

4-  2.7727 
1.3900 
+  3.5861 
—19.2683 

-|-  2.0118 
2.2124 
2.75G6 
+  3.0086 

+  2.8511 
2.9254 
2.944H 
3.3315 

deg.     min.  sec. 

S.  58  52  34.26 
N.62  34  51.81 
N.21  21  59.86 
S.13  56  46.85 

N.15  25  58.12 
N  54  33    3.18 
S.78  27  26.15 
S.  62  14  39.74 

S.  22  32  39.93 
N.39    9    4.18 
S.  10  21  20.80 
N.50    5    1.45 

N.19  10  21.03 
S.59  37  33.93 
N.19  59  12.07 
S.  60  11  37.00 

N.27  43  35.23 
S.  15  23  53.52 

N.74  47    5.58 
S.   8  48  38.53 

N.27  14  11.07 
N    6  54  49  88 

—18.33 
19.24 
19.50 
19.61 

—1999 
20.02 
20.04 
19.99 

—19.92 
19.60 
18.94 
18.12 

—17.89 
17.67 
18.9-1* 
15.12* 

—15.46 
15.23 
14.71 
13.63 

—12.33 
11.74 
10.80 
10.29 

—  9.55 

8.48 
8.32 
7.48 

—  5.03 
4.54 
3.14 

2.88 

—  2.81 
—  0.61 
+  0.40 
+  1.91 

+  2.77 
3.86 
5.05 
+  6.67 

+  8.39 

8.74 
8.55» 
10.74 

A  URS^E  MAJORIS     .... 

J1  LKONIS    

<T  Hydrse  et  Crateris,.  . 

$   TjEONIS     .           

y-  URS^E  MAJORIS    

@  Chamaeleontis,  
«tl  Crucis    .         

A  Corvi    

12  Canura  Venaticorum, 
a.  VIRGINIS,  (Spica,)  
»  Uus^c  MAJORIS,  

&  Ceutauri       .      ... 

«  BOOTIS,  (Arcturus,}  .  . 
a^  Centauri    

&  URS^E  MINORIS 

/8  Librse,  

a  CORONA  BOREALIS,..  . 

£  Ursse  Minoris  

15  49  41  194 

N  78  15  5543 

/gi  Scorpii,  

15  56  29.397 

16     6  16.830 
16  19  58.461 
16  21  55.119 
16  32  25.090 

17     1  55.988 
17     7  37.617 
17  22  55.004 
17  26  57.473 

17  27  47.219 
17  53     1.955 
18    4  33.276 
18  22    0.703 

18  31  43.386 
18  44  23.696 
;18  58  19.965 
19  17  43.88 

19  38  56.27 
19  43  16  12 
19  47  44.86 
;<20     9  30.31 

S.  19  22  44.18 

S.   3  17  35.67 
S.26    5    4.58 
N.61  51  50.58 
S.  68  44    4.75 

N.82  16  52.30 
N.14  34  12.67 
S.89  16  10.25 
N.52  25    3.28 

N.12  40  37.11 
N.51  30  33.50 
S  21     5  36  14 

<f  OPHIUCHI,  

a,  SCORPII,  (Antares,).. 
H  Draconis 

A  Trianguli  Australis, 
e  TJrsse  Minoris,  

at  HERCULIS,  

a.  OPHIUCHI,  

<f  URS^E  MINORIS,  
a.  LYR..E,  (Vega,)  

N.86  35  42.58 

N.38  38  35.33 
N.33  11  14.80 
;N.13  38  20.49 
N.  2  48  43.64 

N.10  14  31.50 

N.  8  27  54.32 
N.  6    1  33.90 
S.  13    1     4.19 

/2  LYR^E,  

£  AQUIL^E 

£  AQUILaF 

y  AQUIL^E,  

«.  AQUIL^E,  (Altair,)  .  .  . 
$  AQUIL^E,  

«2  CAPRICORNI,  

TABLES. 


Star's  Name. 

ti 
£ 

Right  Ascen. 

Annual  Var. 

Declination. 

~~1 
Ann.  Var. 

2 
5 

1 
5.6 

3 
3 
3 
3 

2.3 
3 
2 
3 

1 
2 
4.5 
3 

h.      DI.          s. 

20  13  25.814 
20  16  31.309 
20  36  11.005 
20  59  59.947 

21     6  23.073 
21  14  53.940 
21  23  26.875 
21  26  39.120 

21  36  37.346 
21  57  52.326 
21  58  29.837 
22  33  46.976 

22  49    7.531 
22  57     5.584 
23  32    1.736 
23  33    4.581 

4-  4.8046 
—52.1273 
+  2.0418 
2.6908* 

-h  2.5486 
1.4163 
3.1628 
0.8059 

+  2.9441 
3.0831 
3.8134 
2.9837 

+  3.3095 
2.9776 
3.0569 
4-  2.4042 

deg.     uiin.     sec.       ' 

S.57  13  19.50 
N.88  50  53.54 
N.44  43  57.43 
N.37  59  42.08 

N.29  35  53.03 
N.61  56    4.55 
S.    6  14  44.46 
N.69  53    7.21 

N.  9  10  17.35 
S.    1     3  56.72 
S.  47  42  12.42 
N.10    1  44.67 

S.30  26  12.28 
N.14  22  40.12 
N.  4  47  30.74 
N.76  46  22.01 

4-  17.03 
11.22 
12.64 
17.48* 

4-  14.57 

15.07 
15.56 
15.73 

+  16.26 

17.28 
17.30 
18.65 

4-  19.11 
19.31 
19.36* 
4-  19.92 

611GYQXI,  

Cygrni,  

/3  CEPHEJ,  

i  Pecrasi   . 

«  Gruis 

a  Pis.Kvs.(Fomalhaut), 
«  PEGASI  (Markab),  

y  Cephei,  

Those  Annual  Variations  which  includes  proper  motion  are  distinguished 
by  an  Asterisk. 


SUN'S  RIGHT  ASCENSION  FOR  1846. 


ly 

Mo. 

J:i  miary. 

February. 

March. 

April. 

May. 

June. 

1 

5 

10 
15 

20 
25 
30 

h.  m._.  ec. 

18  46  52 
19  4  30 
19  26  21 
19  47  57 
20  9  17 
20  30  19 
20  51  0 

h.  min.  SRC. 

20  59  11 
21  15  22 
21  35  18 
21  54  54 
22  14  12 
22  33  14 

h.  min.  sec, 

22  48  17 
23  3  12 
23  21  40 
23  40  0 
23  58  14 
0  16  25 
0  34  36 

h.  min.  sec. 

0  41  52 
0  56  26 
1  14  43 
1  33  6 
1  51  38 
2  10  22 
2  29  17 

b.  min.  sec. 

2  23  6 
2  48  25 
3  7  47 
3  27  24 
3  47  15 
4  7  20 
4  27  8 

h.  min.  sec. 

4  35  48 
4  52  12 
5  12  50 
5  33  34 
5  54  22 
6  15  10 
6  35  55 

Day 

of 
Mo. 

July. 

h6  40'  "4 
6  56  34 
7  17  5 
7  37  25 
7  57  33 
8  17  28 
8  37  7 

August. 

September. 

October. 

November. 

December. 

1 
5 
lO 

,  15 

20 
25 
30 

h.  min.  sec. 

8  44  55 
9  0  23 
9  19  29 
9  38  21 
9  56  60 
10  15  27 
10  33  44 

h.  min.  sec. 

10  41  0 
10  55  29 
11  13  30 
11  31  28 
11  49  25 
12  7  24 
12  25  27 

12  29  4 
12  43  36 
13  1  54 
13  20  24 
13  39  8 
13  58  9 
14  17  27 

h  min.  sec. 

14  25  16 
14  41  2 
15  1  5 
15  21  28 
15  42  14 
16  3  19 
16  24  43 

h.  miu.  sec. 

16  29  1 
16  46  23 
17  8  17 
17  30  22 
17  52  33 
18  14  46 
18  36  57 

'ihe  R.  A.  in  this  table  will  answer  for  corresponding  days,  in  other  years, 
within  fouv  minutes  ;  and  for  periods  of  four  years,  the  difference  is  only  about 
eeven  seconds  for  each  period. 


TABLE   III. 


TABULAR    VIEW    OF    THE    SOLAR    SYSTEM. 


Names. 

MAnnHiamPtPr«inlMean  di^ince  Mean  dist.;|    Log.  of 
Mean  diameters  ml  from  the  Sun  thfl  Earth's      mean 

|       in  miles.        dist.    unity.)  distance. 

Time  of  revolu- 
tions round 
Sun. 

Log.  of  1 
times  of 
revolution! 

Sun  .... 

883000 
3224 
7687 
7912 
4189 
238 

[•Unknown. 

1420 
Not  well  5160 
known.   }120 
89170 
79040 
35000 
35000 

37  million 
68       " 
95      " 
144      " 
224,340,000 
226  million 
230       " 
240       " 
246       " 
253,600,000 
263,236,000 
265  million 
490       " 
900       " 
1800      " 
2850      " 

0.387098 
0.723332 
1.000000 
1.52369:> 
2.36120 
2.3788;  > 
2.42190 
2.52630 
2.5895 
2.66514 
2.76910 
2.77125 
5.202776 
9  538786 
19182390 
29.59 

DAYS. 

9.587818       87.969258 
9.859306     224.700787 
G.O.'OOO!)!     365.256383 
0.1828I01     686979646 
0.373100   1324.289 
0.376384   1327.973 
0384  '04   1375.  nearly 
0.402487   1469.76 
0.413211!  I5l2.nearly 
0.425710   1594.721    " 
0442334   1683.064 
0.442725    1685.162 
0.716212  4332.584821 
097947610759.219817 
1.28285330686.8208 
1.4771216012814 

1.944324 
2351610 
2  562598' 
2.836942! 
3.121991J 
3.123190 
3.138303 
3.167300 
3.179547 
3.202700 
3.226086 
3.226610 
3.636738 
4.031718 
4.486953 
4.779076 

Mercury  . 
Venus  .  .  . 
The  Earth 
Mars  .... 
Vesta  ... 
Iris       1  . 
Hebe     1 
Flora     [  * 
AstreaJ  . 
Juno.   .  . 

Ceres  .... 
Pallas  .  .  . 
Jupiter..  . 
Saturn..  . 
Uranus  .  . 
Neptune  . 

TABLE   III. 


ELEMENTS  OF  ORBITS    FOR    THE    EPOCH   OF  1850,  JANUARY  1,  MEAN    NOON   A.1 

GREENWICH. 


Planets. 

Inclinati'n 
of  orbits 
to  ecliptic. 

Variation 
in  100 
years. 

Long,  of  the 
ascending 
nodes. 

Variation 
in  100 
years. 

Longitude 
of 
Perihelion. 

Variation 
in  100 
years. 

Mean  longi- 
tude  at 
epoch. 

Mercury 
Venus.  . 
Earth... 
Mars  .  .  . 

Vesta... 

O       '    " 

7    0  18 
3  23  26 

1  51     6 

7     8  29 
13    2  53 

+18.2 
—  4.6 

—  0.2 
—12. 

O     '     " 
46  34  40 
75  17  40 

48  20  24 
103  20  47 
170  53    0 

+51 

+42 
+26 

75    9  47 
129  22  53 
100  22  10 
333  17  57 
254    4  34 
54  18  32 

+  93 
+  78 
103 
+110 
157 

O             ' 
327  17    9 
243  58    4 
100  47     1 

182    9  30 
113  28  12 
165  17  38 

10  37  17 

80  47  56 

147  25  41 

1     3  10 

Pallas 

34  37  44 

172  42  38 

121  30  13 

327  31  24 

Jupiter.. 
Saturn.  . 
Uranus.  . 

1  18  42 
2  29  29 
0  46  27 

—22. 
—15. 
3. 

98  55  19 
112  22  54 
73  12    0 

+57 
+51 
+24 

11  56    0 
90    7    0 
168  14  47 

+  95 
+116 

+  87 

160  21  50 
13  58  13 

28  20  22 

*  We  give  the  logarithms  in  the  tables,  that  the  data  may  be  at  hand  to  exercise 
tlie  student  on  Kepler's  third  law. 


TABLE  III. 

TABULAR    VIEW   OF   THE    SOLAR    SYSTEM. 


Names. 

Mass. 

Density. 

Gravity. 

Siderial. 
Rotation, 

'  -f  •  and 
Heat. 

Mercury  .  . 

WI**Tff 

3.244 

1.22 

h.       m.         *. 

24      5    28 

6.680 

Venus  

Iffl'zTT 

0.994 

0.96 

23    21       7 

1.911 

Earth  
Mars  ..... 

WAW 

1.000 
0973 

1.00 
050 

24      0      0 
24    39    21 

1.000 
431 

Jupiter  .  »  . 

0.232 

2.70 

9    55    50 

.037 

Saturn  .... 

»*iff-F 

0.132 

1.25 

10    29    17 

.011 

Uranus  .  .  . 

TTilff 
1 

0.246 
0.256 

1.06 
28.19 

Unknown. 
25d.  I2h.    Om 

.003 

Moon  

0.665 

0.18 

27      7     43 

TABLE   III. 


Planets. 

Eccentricities 
of  orbits. 

Variation  in  100 
years. 

Motion_jn  mean 
long,  in  1  year 
of  365  days. 

Mean  Daily    n 
Motion  in 
longitude. 

Mercury  .  .  . 
Venus  

0.20551494 
0.00686074 

-|-  .000003868 
—  .000062711 

O        '        " 

53  43    3.6 
224  47  29.7 

O       '      " 

4    5  326 
1  36    78 

Earth  
Mars  

001678357 
0.09330700 

—  .000041630 
4-  .0000901  76 

—0  14  19.5 
191  17    9.1 

0  59     8.3 
0  31  26.7 

Vesta 

0  08856000 

4-  OOH004009 

0  16  179 

0  25556000 

0  13  33  7 

Ceres 

0  07673780 

—  000005830 

0  12  494 

Pallas 

0  24199800 

0  12  48  7 

Jupiter  
Saturn  
Uranus  

0.04816-210 
0.05615050 
0.04661080 

+  .000159350 
—  .000312402 
—  .000025072 

30  20  31.9 
12  13  36.1 
4  17  45.1 

0    4  59.3 
0    2    0.6 
0    0  42.4 

TABLE    III. 

LUNAR     PERIODS. 

Mean  sidereal  revolution, 27.321661418 

Mean  synodical  revolution, 29.530588715 

Mean  revolution  of  nodes  (retrograde), 6793.391080 

Mean  revolution  of  perigee  (direct), 3232.575343 

Mean  inclination  of  orbit, . 5°  8'  48" 

Mean  distance,  in  measure,  of  the  equatorial  radius  of 

the  earth, 29.98217 

Meau  distance,  in  measure,  of  the  mean  radius, 30.20000 


TABLES. 

SATELLITES  OP  JUPITER. 


Bat. 

Mean  Distance. 

Sidereal  Revolu- 
tion. 

Inclination  of 
Orbit  to  that  of 
Jupiter. 

Mass  ;  that  of 
Jupiter  being 
1000000000. 

1 
2 
3 

4 

604853 
9.62347 
15.35024 
26.99835 

d.        h.        m. 
1        18       28 

3    13     14 
7      3    43 
16    16    32 

O        '        " 

3      5    30 

Variable. 
Variable. 
2    58    48 

17328 
23235 
88497 
42659 

SATELLITES  OF  SATURN. 


Sat. 

Mean 
Distance. 

Sidereal  Revolu- 
tion. 

Eccentricities  and  Inclinations. 

d.        b.       m. 

The  orbits  of  the  six  inte- 

1 

33.51 

0    22    38 

rior  satellites  are  nearly  cir- 

2 

4.300 

1       8    53 

cular,  and  very  nearly  in  the 

3 

5.284 

1     21     18 

plane   of  the  ring.     That,  of 

4 

6.819 

2     17    45 

the  seventh    is    considerably 

5 

9.524 

4    12    25 

inclined  to  the  rest,  and  ap- 

6 
7 

22.081 
64.359 

15    22    41 
79      0    55 

proaches  nearer  to  coincidence 
with  the  ecliptic. 

SATELLITES  OF  URANUS. 


Sat. 

Mean 
Distance. 

Sidereal  Period. 

Inclination  to  Ecliptic. 

1? 
2 
3? 
4 
52 
6? 

13.120 
17.022 
19.845 
22.752 

45.507 
91.008 

d.        h.         m.           ». 

5    21     25      0 
8     16    56      5 
10   »23      4      0 
13     11       8    59 
38      1    48      0 
107     16    40      0 

Their  orbits  are  inclined 
about  78°  58'  to  the  ecliptic, 
and  their  motion  is  retrograde. 
The  periods  of  the  2d  and  4th 
require  a  trifling  correction. 
The  orbits  appear  to  be  nearly 
circles. 

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